This is a 3 part thing, since I don't want to make 3 threads.
1.VoIP integration. Sure, there is getting ventrillo or something to talk with friends/team mates, but since I go solo all the time, it would be helpful to have VoIP integrated into the game. This way, we would be able to communicate better with teammates if they have mics also, and if they don't, at least they would be able to hear you(and mute you if needed). I am sure this one is something that would require a lot of rehashing of code and some major testing, but I would start buying riot points to support the game if this was done.
2.windowed game and loading screen. This one would really be simple and help me out a whole lot. We have all had those games where one person has a terrible computer or a bad connection, and they take ages to load the game. If the game was windowed, we would just minimize the load screen to put on some music, or maybe quickly browse email. Something other than load screen. When you hear nature, you know that the game started. This would also help incase someone has some other program running that they need to keep a tab on, or even to quickly go to the LoL website to quickly look something up. I don't know, just makes sense to me.
3.Matchmaking search filters. This is something that should be %100 done in my mind. Filters would allow us to say what type of people we want to connect with.
-quick search vs nearby matches
-search for people with good connections
-preferred voice chat(if implemented)
-search for people with good records of not disconnecting %95 or more maybe.
So there they are. These things would really benefit the game making things easier and more comfortable for many people.