What are some good shoe options for a RTW trip?

I find your question a bit funny. But since you ask, the answer is no, you absolutely do not have to wear shoe-sandals for your trip. Whether that kind of footwear is the best is highly subjective, but I wouldn't choose those as my main shoes.

This is what I wore for my RTW trip. I walked around a lot, mostly in cities, but also did e.g. some (easy) mountain trekking etc. A definite plus was that the shoes worked fine in restaurants and bars and clubs too.

I also had sandals (similar to these but not as new) in my backpack, for warm places and beaches. I was happy with this choice of shoes. (I certainly didn't have lots of space for stuff; just one 38-litre backpack, i.e. hand luggage.)

My trip took just a couple of months though, and in any case your mileage may vary.

phew This is a question with highly subjective answers.

During travel, and while actually moving from one place to the other I always wear my hiking boots. Usually I have light boots, like the Lowa's "B" class of boots: They have soles that prevent you from slipping, protect ankles, have some hard (rubber-like) protection on the side of the shoe and are padded in all the relevant places. I don't want to advertise any particular brand. You can get these type of light hiking boots from lots of places, and lots of brands. I always wear them when actually moving around with my backpack because they are the heaviest.

I then sometimes - always on the long trips - some very light sandals for the beach and warm areas just as Jonik mentioned already.

Both are bad for any "elegant" ventures. But I never had trouble getting into a restaurant or even casinos. (Well, the more traditional casinos in Germany, where I live, would not let you in with shoes like that).

To be honest, I believe most backpackers don't venture into such "high-class" establishments and therefore don't need "elegant" shoes.

Consider good socks as well: Thick hiking ones for the boots, and thin for elegant shoes.

But most importantly the shoes (and socks) have to be light (for carrying around the world) and comfortable! Take only what you absolutely need.

It depends where you're going and what season it is.

For walking around cities, walking shoes are a good option. New Balance makes some good ones. Make sure they're waterproof, you don't want to get your only pair of shoes drenched in the rain.

For the OP, if you're doing a bit of hiking as well, you can use waterproof trail runners for the whole trip. Salomon and Merrell are some good brands.

If you're staying in hostel, I'd bring a pair of sandals for the shared shower.

For a hot climate like Southeast Asia where you're visiting a lot of beaches, the sandal/shoe hybrid is good. One downside is that some places get really muddy when it rains, and you end up getting street slime all over your feet. So think about bringing a pair of backup "real" shoes.

I agree with Rog182, I still have my Merrell Continuum with Vibram sole after a year of travelling.

I reckon with a pair of trekking shoes *not boots and some sandals you are sorted for most cases.