While watching this current LoL live world championship (Intel extreme masters), I noticed some players play in window mode. Why is that? What are the benefits of playing LoL in window mode?
The answers already given are correct, but in most cases, players use windowed mode cause they are not at home, and they are used to one resolution. Pro players usually play on one certain resolution, and if they have to go to a LAN event, they tend to set the resolution on their PC to the resolution they are used to, cause even small changes can make a huge diffrence (you cant predict the range exactly if you are used to an other resolution).
Obviouly it also helps with Streaming and/or Alt + Tabbing, but the biggest reason for playing in windowed mode (for pros at least) is the resolution.
Windowed mode (or even borderless-windowed mode) has the advantage of not getting the exclusive use of the screen. This is actually good to not disturb Alt-Tabbing for example, or being able to use secondary screen easily.
In case of a one screen setting, it can be useful to activate this to avoid "desktop dropping" when you accidentally hit windows key (if it's not disabled). When your PC allow the overhead in resources, I don't see why you wouldn't use it.
^ The reason to not use it is because fullscreen mode uses 100% of the GPU (graphics processing) on League of Legends, whereas windowed mode uses some on LoL and some on the other programs (Chrome, Word, etc.) that you're using.
With a lower-end GPU, playing on 1980 x 1050 with windowed mode can result in bad framerates, where it would play fine with full screen. Conversely, a good GPU can give good performance everywhere.
I think what you might have seen is the players using windowed mode during champion pick. During the game, you don't see the player's screen, since their game is 2-3 minutes ahead of live (it could give away important tactical informations). So they try not showing it. Players use the windowed mode in champion pick because you don't need fullscreen there.