Since it is my field of expertise, I can offer you the service, that you could write me a PM to ask me about almost any MMORPG out there, wether it's free or not.
Uncharted Water for example is probably interesting at the first peek, but you got to know it is an asian MMORPG. That is no problem at all, if you know the pros and cons of asian MMORPGs. Most of them want to have a huge investment of time, mostly spend grinding (killling monsters without quests and/or reward). If you are looking for a MMO in which you can have a ship I would recommend trying out Kartuga first. It is under no circumstances perfect, but I certainly doesn't need a lot of time sunk into it and you can still have fun playing it.
Going through the other suggestions, I can offer some tips too. You should not play Eve, if your not totally into Science Fiction and making your own story and way through a gaming world. It is a really hard thing to get used to. Yes, the game has quests and stuff, but really the fun of Eve is venturing through the universe living and breathing it. It is true sandbox MMORPG giving the players loads of freedom. But that can be good or bad.
I don't like guild wars 2. It is trying to innovate and cover up tracks. It says no questing, which is not true. Only because you got no NPC I've to talk to, you ain't got rid of questing. I love quests, don't get me wrong, but I don't like it, when somebody tries to sell me something there is not. As an old MMORPG player I am used to the holy trinity, which means a tank up front, damage dealer all around and healer in the back. Guild Wars 2 tried to get rid of it, which endet up in everyone pillaging bosses with no need for tactics (besides hopping away from AoE). Even if you get hit and die, anyone can ressurect you in combat anytime. One think I really like is the combat system, but I really don't like the classes in GW2. So I would recommend Guild Wars 2 as an entry level mmorpg for starters.
Neverwinter Online is not really on MMORPG per se. It is more like an action copy of something more or less looking like an MMORPG. It only got corridors no really open world. It's action combat and the possability to make your own dungeons are pretty neat though. You should try it, if you dont want to explore a lot and get into action fast. I liked Dungeons and Dragons Online more somehow. It stayed closer to the IP I think and felt better that way.
Secret World is awesome in the beginning, but I know it looses a lot in the end game. Still it is unique in its setting. I would always recommend anyone who liked the trailers to go try it out. It does exactly deliver what is promised (allthough the quests do get worse in the end, meaning less creative).
Rift and Star Wars Old Republic are really just copies of World of Warcraft with some new mechanics hidden somewhere. I really didn't like star wars, because the combat did just feel wrong. When I think of jedi fights I think of awesome action and cool moves, but in Old Republic standing in front of each other exchanging painfully slow moves waiting for the global cooldown until you can make the next one was just a huge bummer. Definitly no recommendation from me.
Rift as I said, just WoW with a slight diffrent look and the mechanic two switch inside your class between skill trees. It is nice, just watch the trailers and you know what you get.
Some recommendations no one mentioned would be:
Maple Story, which is just freaking huge. It has really creative classes and if you like 2D games it might be worth a try.
Tera, action combat, good for any starter who likes really good graphics and a nice combat system.
Lord of the Ring online. One for the Fans of the books and or movies.
There are countless more games, just feel free to ask ! :)