Love anime, more so than pretty much every entertainment form out there, though there's a lot of crap out there. Bleach to me, is a perfect example of popular crap. It's 360+ episodes; can have an incredible slow pace (at least during the arc I watched it was); at least 100 episodes of fillers, and pretty much every filler arc is consider crap by the actual fans of the show; loads and loads of characters, the vast majority of them boring; surprisingly dull fights, not that awesome ones don't appear, they're just diluted in a sea of crap; the OST's pretty good, at least OP/ED wise; and most importantly the anime doesn't even finish where the manga does (which can lead to either gecko ending, no ending, or a poor one that doesn't give a sense of closure, I have not seen it as I hate Bleach) as it was cancelled due to bad ratings (filler arcs were the cause). Manga-wise, they finally entered the last arc which from what I understand, will last roughly a decade. Even by Long Runners standard that is utterly ridiculous. Rant over.
Here is a list of anime I would suggest . . .
Case Closed ~ I hate subs, and even if I didn't six hundred plus episodes are just too much for me to invest time into. However the overall arc of the show isn't really important, from my knowledge he's had very little progression except teaming with FBI agent or something. It's episodic and normally always enjoyable. I haven't seen all the dub episodes, nor do I feel the need to, but watching it always guarantees time well spent.
Cowboy Bebop ~ No I'm not doing this in alphabetical order. If you haven't watched Bebop, this is the first one to watch. People who hate anime, love Bebop . . . it's that good. To paraphrase JesuOtaku "It's a show that style over substance with more substance than 90% of other shows".
Baccano! ~ You want have a damn clue what's going on in the first episode. The following episodes will make more and more sense, as the story is told through the different characters (the OP alone feels 17 characters are important enough to pause on them and show you there name . . . and there are plenty of more than just 17) and two different years. The narrative after episode one is mostly linear within it's own year and is incredible. The characters are incredible. Isaac & Miria are in my opinion hands down the funniest characters in anime history. Ladd Russo, Claire Stanfield, Firo Can'tspellhislastname, Jaccuzi Splot, etc. are all awesome. It's only 13 episodes, with 3 more DVD exclusive episodes that take place after the series (And are worth a watch, if just for the last episode) so it won't take long to get through it and it's worth the ride.
Death Note ~ You've probably heard about this one, as it get's a lot of hype. The show is incredibly smart, and reinvents itself multiple times through the course of the series. Not to mention, this series gave us L, who is in my opinion the smartest character in anime history (sorry Kudo), and not only that but he's one of the most original characters you'll ever see in anime. The series is worth a watch just for him, but I love more than just him. The show can be best describe as two chessmasters (yes, I use a lot of TV Tropes phrases) going up against each other. The first 25 episodes of the show are incredible but from there it becomes terrible. However the last two episodes are back up in quality and are amazing. The last episode is still quite possibly the greatest ending to an anime I have ever seen.
Both Fullmetal Alchemist ~ I prefer Brotherhood, but watch the 2003 one first. The reason being is the first twelve episodes of Brotherhood cover the material from the first series but they rush it and ruin a lot of what made those episodes awesome and impactful. The rest of Brotherhood more than makes up for that, but trust me, 2003 then Brotherhood is the way to go. I'm not even going to give reasons to why one of the most popular and critical acclaimed anime franchise should be watched.
Monster ~ One of my favorites, and the only one that is realistic. It's 74 episodes but it never decreases in quality. It only get's better and better. Though there is a period where it gets a bit worse but it's still high quality. The final arc of it was definitely the best though. It's just incredible a show can stay that great for so long. The show begins really slow paced, I believe it takes three or four episodes before the shows real plot get's kicking, but it's well worth to go through it.
I have other anime to suggest but I'm lazy and don't want to bother writing up reasons (I'm assuming you've seen DBZ so it's not on the list) and I doubt you want to read them so here you go; Yu Yu Hakusho; Deadman Wonderland; GetBackers; Gun X Sword; Samurai Champloo; & Trigun.
As a personal code, I'd rather not recommend a series I haven't completed, so I didn't. I have over 50 animes on my to watch/finish list, so I should have a ton more to suggest later.