There are so many FTPs out there that are wonderful, but my 2 favorite are; Team Fortress 2 and World of Tanks. Both of these games are very popular as FTPs and there is reason to it.
Team Fortress 2 you can pay for add-ons, but the base game is free. The games has good variety, classes are very different from each other and you need to play each one by strategy, so you actually have to be good at the game to do well, which is what I like about it. There are unlocks in terms of weapons, apparel, accessories etc. and this is what makes it one of my favorites; it is very customizable.
As for World of Tanks, I don't play it an awful lot but it is a very good and quite addictive game. Again, a lot of variety in terms of tanks and the gameplay is unique. They did a good job and I don't see anymore free tank games coming round soon that will top this one.
Regirock, the Rock Peak Pokémon. It can use rocks to repair its own body.
Starwars the old republic, Last Chaos, Runes of Magic, and Global Agenda are me favorite FTP MMOs.
Happy wars, League of Legends, and Team Fortress are my favorite free normal games, though TF may count as an MMO...
Admittedly I don't enjoy free games much, I prefer just playing Starcraft (player made maps are free thus it is very fun to play those "free" games. This is due o the powerful map editor they give that also allows someone to script things)