You really have to define what you don't like about "Pay to win". In a PvP MMO, yes, it sucks to go up against other players that bought their way into beating you. In a PvE MMO, who cares? So the dude bought an experience booster and leveled to 50 in one day....why do you care?
So based on that, i'd first look into whether the F2P MMO have a good PvE section. Games like DDO (Dungeons & Dragons Online) and LOTRO (Lord of the Rings Online) are predominantly PvE and that is where they shine. LOTRO is probably the best quality F2P MMO out there. Yes, their store is gigantic with a ton of things that you need or can buy, but that is because LOTRO have a ton of content with like 3 or 4 expansions out.
Games like Aion which have always had a big PvP undertone , there you will always feel people are buying themselves into better characters which directly impacts you.
Star Trek Online and Champions Online , are also pretty much PvE games, so they should be ok too.
DC Universe Online also went F2P not so long ago, and while it's alot of fun, it has a very big PvP influence. So unless you purely play on a PvE server, it might be frustrating.
Of course, City of Heroes/Villains (also F2P) might be a better PvE experience than DCUO if you're into super heroes. However it is quite an old game and not as actiony as DCUO.
So ultimately i'd judge a F2P MMO based on how much the store will enable players to influence my personal game play (negatively). Usually this only happens in MMOs that "devolve" into a heavy PvP end-game. World of Warcraft is an example of an MMO where i predict, if they were to go F2P with their heavy PvP end-game would make for a very controversial and negative experience combined with a full cash store.
Even Guild Wars 2, is still up for grabs what will happen there. Guild Wars 1 has a huge PvP / Arena section of the game with relatively short PvE campaigns, and Arenanet only much later started adding cash shop to Guild Wars 1 (so it was not part of the game design) . They will have to be very careful with Guild Wars 2 since they WILL have a cash shop and it WILL be part of the game design....
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