I like to watch a lot of "slice of life" animes (School Rumble, The Melancholy of Haruhi Suzumiya). I find them entertaining and get myself caught up in the story. Of course, I also like a lot of the serious anime (like Death Note) that are very smart and make you think.
Normally I can only watch things with supernatural aspects in them. Action is also nice. Not to big on the slice of life or romance ones unless they're original or really well made. Shows like Angel Beats are perfect for me, action yet not overkilled, good plot, nice characters, sad yet funny still at times. Was very good.
I started with the action packed ones, but then started to go more for the romantic and slice of life themed. For the most part, I only like if it has: 1. science fiction 2. action: usually involving the science fiction 3. cute girls. If it doesn't have, then I don't usually stick with it. But there have been plenty of exceptions.
Horror/Psychological, but unfortunately there aren't very many good horror anime out there. I usually take a bunch of shows from the current airing season and watch them (since its one episode per week its easy to keep up with multiple shows). I also like comedies, some slice of life, and action/adventure. I particularly enjoy anime that are between 12-50 episodes (only around 50 if its a really good series, but very rarely does that happen).
I don't watch too much anime, however, i will usually watch the anime that i've already read in the manga, so mosty shonen mainstream. I'm a kinda bland fella...
I like Japanese anime, such as Digimon and Pokémon, because of how the character designs are, as well as the background tracks that they use.
I like the action animes more myself, but like them to have a good amount of humor. FMA and Soul Eater to name a couple. Of course I liked the first few seasons of pokemon and yu-gi-oh as well. I've only relatively recently gotten more into anime, so I'll broaden my scope later.
When it comes to anime. I've adopted a 5-star rating system based on Concept, Story, Music, Characters, and Quality. It's very rare that I get an anime that scores full points in each category, but I like watching anime either way, so it's all good.
I enjoy anime of the psychoanalytical variety. For your needs, however, Baccano! sounds like just the thing.
I'm pretty sure I don't watch as much anime as the rest of the people on here do. Not anymore at least. I still stick to a few, namely Blood+, Kuroshitsuji, Alice Academy and Ouran High School Host Club. Manga is a whole 'nother story. In general, mainly the ones with complex story lines where you have to think about practically everything so you can fully grasp it's story. I like them very unique. I'd pretty much say stories of which are from the animes: Blood+ and Air Gear (for the story, note that. I know there are some scenes in Air Gear I wish I'd rather have never seen). I also like dark, supernatural or magical anime. Those always interest me. But my main point, probably is how the art is done. I'm quite picky when it comes to the art. If it appeals me, I'll like it so much more because it will inspire me to draw and stuff. Voice acting/music is also important because some voice overs I can't quite stand - i'd rather hear them in their original Japanese with the subtitles. I do enjoy sweet, comedic or romantic anime as well though I probably wouldn't stand to them as long. The longest perhaps of anime under that category would be Ouran High School Host Club, because I just love it so much. Ha ha.
hentai I enjoy many anime, and none in particular. However, of the ones I enjoy the most, it's romantic ones, action packed ones, anyone with a good plot or a character I can relate to. I simply love Death Note, which I guess is a psychological one.
I enjoy a lot of anime, but I'm not sure I like a certain kind. Basically it just has to have some kind of fighting for the most part, but I guess that's not entirely true since I like a bit of death note. If you can find something common between Bleach, One Piece, Yuyu Hakusho, Naruto, My-HiME, and things like that let me know, because I just watch anime a lot so I don't know what's entirely in common with them