Highest on my priority list are rare gems like Bartender, with intelligent, well-crafted stories. Gankutsuou and Blassreiter are also good examples of stories like that. A good, fun comedy like Hayate the Combat Butler is always appreciated.
I'm also a big fan of sci-fi and mecha anime in general and the Gundam series in particular.
I also enjoy anime that are about topics rarely covered by anime in general, like economics in Spice and Wolf.
Action anime are lower on my totem pole, despite Bleach being my favorite anime. This genre is usually a toss-up depending on the story or other things, though usually I go for over-the-top overpowered anime like Needless or Sengoku Basara.
Lowest on my list are ecchi-centered love comedies like Ladies vs Butlers and random brainless humor like Baka to Test.
Lastly, I'm not one to start watching shows that got good reviews and not consider watching shows that got not-so-good reviews. I'm not one to be swayed by rankings; I prefer watching a show for myself and judging it instead of letting others do it for me.
Feel like recommending? I'm always on the lookout for some food for thought shows. You can always leave me some notes :)