What are some tricks you use to buy cheap airline tickets in Europe?

• Ryanair allegedly shows different prices to based on your previous visit / search history to give you the illusion that cheap tickets are running out. Clearing your cookies or visiting the site in incognito / private mode can show you the truly cheapest price they have.
• Flying out in the middle of the week is a good strategy for almost any kind of air travel. Of course, that's not always possible and sometimes you do have to fly on weekends. On those occasions, try to structure your flights in such a way that you catch the flights with low load factors. Say there's a football match in Germany on a Sunday and you're flying out of London. Then you can be certain that flights to that city on Friday / Saturday to that city will be expensive, and the same for flights returning from there to London on Sunday. This is just an example but it's valid for many scenarios. Which direction of travel sees more traffic on any given date? Then avoid that day and choose something else.
• Following the above point, learn to do a 'broad search' for flights. Sites like SkyScanner, Kayak's Explore and many others can show you trends in where flight prices are heading. Both SkyScanner as well as Kayak show fare graphs of price trends (on Kayak, this is available under the link 'Fare Graph' after you have searched for a flight.)
• Mixing airlines, i.e., flying one airline one-way and another on the return journey. This is valid mostly for low-cost airlines since with them, it doesn't matter whether you book one-way or return flights - the price will always be the same. (With full-cost airlines, one-way tickets get charged a premium; return flights are cheaper.) So for instance if you know both Ryanair and Easyjet fly a particular route, add them up individually to see whether booking separate one-way tickets with them is cheaper.
• Sometimes, it is worth checking fares on standard airlines too and not just low-cost ones! This is especially true closer you book to the date of departure. Low cost airlines can sometimes be costlier than discounted tickets from a full-service flight (once you factor in that you'll be paying extra for luggage as well as booking fees).

I've faced this same problem before. I spent 5 years in Europe, and traveled quite extensively. Navigating Ryanair's website can only get you so far (literally). Once I learned about other cheap airlines, I tried to figure out the best way to ENSURE I was finding the cheapest flight.

I wish I could tell you "use Kayak" or something, but as far as I know, there is no catch-all tool. The best tip I could give you is this:

Choose your destination, look up all the airports within an acceptable distance, and navigate the airport's website for what airlines it serves. From there, you can start down the path of identifying those airlines that best suit your needs, and your pocket book. Remember, a lot of destinations have multiple airports, and most cheap airlines serve the "b" and "c" airports.

For example: want to head to Berlin? Searching Berlin's 3 airports for airlines they service will lead you to Air Berlin. A large percentage of Air Berlin flights are very comparable in price to Ryanair, and they flight to a ton of destinations. If you are like me, you've heard of Ryanair, but not of Air Berlin, so mission accomplished.

Another tip: When you are on an airport's website, look for transfer buses that get you into the city on the cheap. For instance, flying Ryanair into Frankfurt actually lands you about an hour's drive from Frankfurt. There is a bus that will take you into Frankfurt proper for just a few Euro.

Price is often a function of convenience. As another answer notes, " look up all the airports within an acceptable distance" -- but that acceptable distance might be hundreds of kilometers. Maybe it's significantly cheaper to fly to Faro and take a three hour bus ride to Seville (I just checked such a trip). Is it worth it? That's entirely your decision. Check for connections though, distances are deceiving, for example there might be a high speed train, like from Rome FCO to Florence and on while Milan MXP doesn't have a direct train there.

I also do not see azair.eu mentioned here. It's frighteningly good and much less known than even Skyscanner not to mention Kayak.

Know your airlines.

1. Leaving in the connection city (i.e. middle city) - Air Berlin, Tarom, Czech Airlines.

   For example, a ticket Bucharest - Berlin on Air Berlin was 240 Euro, but a ticket Bucharest - Berlin - Frankfurt on Air Berlin (with exactly the same first leg) was 60 Euro. So if you need to fly to Berlin, you buy the through ticket, exit the plane in Berlin and don't come back. If you want to be really nice, tell the gate agent that you're not coming, so they wouldn't wait for you. This strategy carries some risks, but in my experience they never realized. Note that this is against some airlines Conditions of Carriage.

2. Throw-away return (KLM, Lufthansa, Czech) - one way ticket usually comes from a different (more expensive) fare class, and thus such tickets are more expensive. Adding a return flight somewhere in Oct or Feb in the middle of the week might drop the roundtrip price well below the one way price. For example, one way direct Bucharest - Prague could be $400+, but with return it could be $180. If you want to play by the rules, you can call them later and cancel the return leg. This could be combined with low-cost flying the return leg to achieve the needed price+schedule combination.

3. http://google.com/flights or SkyScanner with "Europe" as a destination, if your destination is flexible (i.e. you want to go somewhere for a weekend, and don't really care where to go)

If you often travel with a company that has a loyalty plan, you may be eligible for exclusive discounts including free of charge travel. You can save more points by buying tickets for other people from your account. So, if you have many friends who travel frequently, you can set up a collective account that is formally owned by one of the members. This person then gets all the points, but you can then share the benefits. Not everyone will be traveling at the same time, so there will be plenty of room for everyone to benefit from the exclusive offers.