This is a bit of an old question, but as an industry insider, I thought it was worth answering, because the real reason that one-way rentals don't exist between Alaska and the Lower 48 hasn't been touched on by anyone else.

My experience: I managed one of the major rental companies in Anchorage for the better part of a decade.

Why is it not possible to find one-way rentals to or from Alaska? Because the majority of rental offices in Alaska are owned by independent licensees.

Franchises own their own rental fleets. They buy or lease their own cars separate from the "floating" corporate fleets that cover most of the rest of the United States. (The company I worked for sourced vehicles from several different places: direct deliveries from manufacturers, bulk deals from local dealerships, "program" cars from leasing agencies, etc.) As the legal owners (or lessees) of the cars, they take delivery of the cars directly from the sellers/lessors via auto carriers. They then run the cars in their fleets for the applicable amount of time before defleeting them in the form of local retail sales, auto auctions, lease returns, etc.

So there are three reasons that one-way rentals to and from Alaska haven't been offered:

1. Purchasing (or leasing) new cars means that the owner/lessee needs to take possession of the car. There wouldn't be an easy way for a third party (such as a corporate-owned location or separate franchise in the Lower 48) to take possession (and responsibility) of a new car on behalf of an Alaska-based owner, especially without a guarantee that the car will end up making its way to Alaska.
2. For an Alaska-based franchise to in-fleet a car owned by a rental company in the Lower 48 for permanent use in its fleet, it would effectively have to purchase the car from the existing owner. Avis or Alamo Anchorage relying on purchasing one-off used cars from Avis or Alamo corporate in questionable condition at random prices isn't exactly a seamless process or sustainable business model.
3. Ultimately, the demand for one-way rentals up and down the Alcan Highway, especially during the months that it would benefit the Alaska operations, is a drop in the bucket compared to the in-fleeting and out-fleeting needs. When the typical rental office in Anchorage needs to procure on the order of 500-1,000 cars during the spring months, the (at most) few dozen people who might be interested in one-waying a car from Seattle to Anchorage isn't going to materially affect the number of cars coming into the state. Add in the logistical complications of in-fleeting "foreign fleet" cars, and it's much simpler to just get them delivered new--especially when the seller absorbs the actual cost of shipping above the "destination charge" (the same amount is charged by manufacturers nationwide--it's the same $600ish fee you see on your new car window sticker anywhere else in the country).

Things might have the potential to change in the future, though, because more Alaska rental offices are becoming corporately owned. As of a few months ago, now four of the seven brands located at the Anchorage airport--more than half--are now owned by corporate. With more locations now featuring at least the technical capacity to move cars between locations, it's possible one may experiment with allowing northbound rentals in the spring and southbound rentals in the fall (the Alaska market is highly seasonal, with the vast majority of Alaska's million-plus tourists coming between June and August). You'll want to keep an eye on Hertz, Enterprise, National, and Alamo, which are corporately owned--the other major brands present in Anchorage remain franchised. But for now, the solutions recommended in the other answers--one-way rentals of RVs and U-Haul trucks--are the best solutions for someone seeking to drive the Alaska Highway in one direction.

One way car rentals tend to be limited to areas where there is regular demand for such rentals, and thus a good chance someone will return the car back to its original rental region. So you will see one way options within the continental US, but not Alaska to the continental US, as the number of folks wanting to do a one way car rental is extremely small.

The major car rental companies may occasionally have a car they need re-positioned to the lower 48, but that is just the luck of the draw, not something you can reserve. Local rental companies in Alaska would never rent one way as the re-positioning costs would be quite high and they have no drop off office.

The exception to this rule is RVs, as there are one ways available from some companies (Cruise America is one). There are also delivery runs for RVs going in both directions (bringing new RVs to Alaska in the spring, taking used ones back down in the fall).

There are drive away services that hook up drivers with people wanting to send their car or truck somewhere else. Though not sure how many offers you will find from Alaska down.

As other have mentioned, U-Haul does one ways, but that means driving a big truck and I assume your goal is sightseeing between Alaska and Seattle, not simply driving straight through.

I did a multi-site search on Kayak, Hotwire, Priceline, CarRentals.com, rentalcars.com, Expedia for a ttrip between Anchorage and Seattle. All search results returned empty.

Looking at smaller car rental companies in Alaska also failed to find any cars offered for driving to Seattle. It's not particularly surprising considering someone will have to drive 3700 km across desolated roads to get the car back to Anchorage.

Other possible options include renting a U-Haul truck, buying a used car in Anchorage and selling it in Seattle, or posting an advertisement on Craigslist offering to drive someone's car to mainland US.

There's no "universal" policy restricting border crossings through Canada, but it's not universally available from every rental location. Large nation-wide chains may be the best bet, like Avis & especially U-Haul (that specializes in one-way moves).

The best way to find one is probably to start asking every rental agency in Anchorage directly (phone, web, email, etc) since it appears to be up to their discretion if & when they have such vehicles available. A web search (like here or here) should find ample rental locations.

U-Haul will rent you a truck to drive from Anchorage to Seattle, you can book a truck online at uhaul.com, thought it might be very expensive ($1700 US). And according to these guys (at least a few years ago) Avis would "occasionally do one-ways south at the end of the season, though--try emailing them at reservations@avisalaska.com or calling them at 907.243.2377." So it is possible, but every company I've seen advises calling them directly to inquire.

Or an RV should be available to rent one-way too. https://www.bestofalaskatravel.com/ offers one-way rentals for currently (2016) a "One-way drop fee" of Anchorage to Alaska $1,259 or $1,049. (One-way drop fees are in addition to the per day rates of $109 to $279)

I've read that actually crossing the borders one-way is common & not a big deal, even with a rented vehicle & trailer, especially if you have a list of everything in the trailer ready. The "Border Security" tv show mentioned below even had an episode with two brothers who rented a U-Haul cube truck in Mexico (because of age restrictions on rentals in the USA apparently) and were driving it all the way to Alaska (haven't found the episode or a link yet).

• Alaska Hiway Road Trip - Rent Car in Canada-Drop Off in USA?

  >> I am seeing that it may not be possible to rent a vehicle in Canada and drop it off in the United States. <<

  No, it's possible and done all the time, BUT it works only between locations where the rental car companies will allow it, generally those that have a big enough demand for cross-border rentals so that returning the cars to their country of registration (US or Canada) is economically viable. You can easily pick up a car in Seattle and drop it in Vancouver, or pick up in Vancouver and drop in LA. Picking up in Banff and dropping in Salt Lake? Good luck with that. Pick up in Edmonton and drop in Fairbanks? Not likely.

  As stated there are a couple of RV rental companies that reposition their rigs in the spring and fall, to/from Alaska from/to the lower 48. And Avis in Alaska often has good deals on repositioning cars from cruise ports, typically Skagway, to Anchorage at the end of the cruise season so they don't sit all winter with no business. But those are the exceptions.

  Intra-State (Haines to Anchorage etc.) otherwise typically have very high one-way drop fees; by the time you look at your (yes, convoluted) plans and add dollar signs, you might be better off thinking about driving your own car all the way, then if you want to get back without retracing your steps, look at shipping it on TOTE from Anchorage to Tacoma, and fetching it there. That's what many Alaskans do, e.g., when being relocated by the military, or kids going off to college.

Another Option - buy, drive & sell a vehicle

If you have a little time & can find a vehicle for sale, then buying it in Alaska and driving it "home" to Seattle and selling it there may be a viable alternative. (A good "breakdown" plan like AMA, etc may be a good idea too.)

• http://www.flyertalk.com/forum/alaska/743958-renting-car-seattle-alaska-trip-2.html

  I figured out a way out of this conundrum. My job only gave me 9 days off in a row so I bought a cheap minivan in Reno Nevada, and arranged a buyer for it in Anchorage. The girl was so happy to get a vehicle with no salt damage and one that was apparently road worthy enough to make it. Of course if we had broken down on the way we would have been in a pickle--but it worked!

Border Crossing related Info

Here's some general tips about Driving a Rental Car across the US/Canada border I found from a web search, sounds useful:

• Make sure you have all the normal required documentation for a border crossing such as passports and drivers license. Driving a rental car plus having document issues will probably make for a slow crossing and additional interrogation.
• You must let the rental company know you are going to take their car out of the country, and they must confirm it is ok. You will be violating your renters agreement if you don’t and all kinds of very expensive problems will come up if you get a ticket or have an accident. In addition, U.S. Customs actually requires that the rental company has given their consent for the car to leave the country so it had better be in the rental agreement.
• Auto Insurance – Most auto insurance will cover you in both countries but you should absolutely confirm this with your provider. You must always carry your usual insurance card but you may need to get an insurance card for the country you are visiting as well. Your carrier should provide this at no charge. If you take out the rental agencies insurance they should issue you a non-resident insurance card which must be kept in the rental vehicle.

Here's a little scary info about the worst case scenario that could remotely, possibly happen at the border, a possible reason why companies may want to restrict border crossings in their vehicles, with videos you can see for yourself.

There's also the remote possibility that the border crossings could go badly for you, as well as the car rental company. There are "Border Crossing" tv shows, like "Border Security" for Canada (link to youtube search) & Australia, where you can watch them rub a sample cloth over items (like the outsides of luggage and vehicle seats) and have their machine say there's "drug residue" on the item. No measurable drugs, or even anything visible required, so would look spotlessly clean. One agent (in this Season 1 Ep 13 video from 8:40) even says "once we find an indicator for narcotics we do 'step it up' and look in personal [belongings]" (can also watch the woman a few minutes earlier get handcuffed, detained and thoroughly searched because she says "I'm not sure, but I think I know" what's in her luggage; imagine saying that truthfully about a rental vehicle). And as can be seen on the shows, and wikipedia agrees, "persons can be denied entry into Canada on the basis of suspicion alone."

Therefore, if there's even any invisible "drug residue" in the vehicle or your stuff the border agents could detect that, and then you get extra attention (searches, questioning, etc). In the worst case scenario you could be in trouble, and have the car possibly torn apart in a search or even seized. It's a remote but non-zero chance, but could be very expensive. In my personal opinion, I would think hard before driving someone else's vehicle across a border.