What attracts me most in MMOs is small group play, be it PvE or PvP. The 5-man heroics in WoW during the TBC era felt like they were made for me (esp pre-nerf). Wiping for 2-5 hours on trash in Shattered Halls with a dedicated guild group (read: good friends) must be one of the most awesomest experiences one can have behind a computer screen. WAR battles were a bit too massive for me, as was AV. Tactical PvP scenarios a la Arathi basin (wow) or some of the WAR scenarios (Nordenwatch, Isha's temple) also make for a lot of fun for me. Arena PVP is often too static, not chaotic enough, and with too few people for my taste.
Levelling professions (collecting recipes, I can obsess about collecting stuffs ingame) and having a cool, working, economy adds to the entertainment for me, but it's not the most important thing (if it was I'd still be playing Eve)
Turnoffs are class dynamics that aren't quite right (tanks keeping aggro too easily, healers being able to heal too much or not enough, dps that doesn't need to balance their damage output with either threat or self-inflicted damage), a generally impolite community, hmm. I know I can think of more....
Edit: And what Mac stated so eloquently and so much more concisely than me, below!