I'll start by saying that I have only experienced a handful of PWs: Dammendrech (played there for about a year and a half), Dasaria (been playing there for half a year), Sea of Dragons (played there for a month) and Dalelands Beyond (a few weeks). I've tried a couple of others, but too briefly to judge. Now, to the survey:
1) All of the aforementioned servers are/were RP worlds, so that's the section I tend to look at. I'm primarily attracted by the lore, setting, atmosphere... That's what I liked the most about Dammendrech and it's still my favourite PW ever. To put another example, I tried Xenograph once, though briefly, because I wanted to see how a futuristic PW would look like. Quality of RP between players is also very important, but that comes without saying and you can't experience it until you're actually there.
To a lesser extent, there are some mechanical features that may attract me: I'm generally not a great fan of neither epic levels, nor of classes' additions, restrictions and so on (Dasaria is a good example of this, and so was Dammendrech). However, the most popular PWs are level 30 and have Kaedrin's classes, so my view is probably not the majority's here.
2) Population. Take out people and multiplayer loses its function. I'm actually not that fond of PWs with 50+ players, but a decent one is necessary. Dasaria's population is relatively low in comparison to other PWs, but it does the job. Dammendrech's was very, VERY low when I played, and this ultimately lead to the server's death.
I agree with kevL about having quests or some kind of stuff to do when you are alone or not feeling too social (or just want to kill something for a change of pace). Dasaria, even though it's aimed at parties primarily, has a lot of quests (repeatable after every reset and soloable, providing you survive) all round the server, and I think this is a good way to do it.
DMd events on a regular basis, good RP quality between players (including factions), friendly/welcoming players and staff, etc.
3) The opposite of any of the above, I guess. Population in the first place. If everytime I look I see zero players on, I'm better of playing a single player module. If I log and everyone's a jerk, they can go jerk themselves (not that I've really have any experience with jerks when trying a new PW, but it's a possibility).
"MMO feel": OOC as a standard and players running around like headless chickens trying to be the first ones to get the Sword of Doom +5000. Level 40. Level 50. Epic relevels (in Realms of Trinity I think), however that works.
If I think of something else, I'll post it later. I have to go now.