I'm going to have to second Attack on Titan. I can see why it became so popular, it does a lot of generic 'awesome' things, but the pacing is shit, there's almost no creativity involved... It's a psychological show where the characters are flat caricatures instead of realistic people. It's a military show with idiotic tactics. It's a mystery show in which nothing will ever be explained and the viewer is punished for trying to think about things too much. It's an action show with maybe 30 seconds of things happening, and then 20 minutes of people talking about them (saying the same things over and over, or just cutting to a copy-pasted reaction face for a minute straight). And all this goes on and on forever...
Elfen Lied is right out. I liked the manga, but then the animated adaptation screws up every character, removes every scene that doesn't include blood or tits, butchers the story, and just generally slaps the title and a few visuals of a good story onto the lowest common denominator of "entertainment".
I'd stay away from all the "endless shonen", like Bleach, Dragonball, Naruto, One Piece, etc. They start with a stupid, repetitive, boring manga. And then they add about 70% by volume of filler. And then they keep this up for hundreds and hundreds of episodes. I'm not sure I've seen anything that went on for over about 63 episodes (however long FMA: Brotherhood was) without being shit, and refuse to start anything over about 26 without very good reason. Hunter x Hunter wasn't terrible for the few episodes I watched, but it wasn't good enough to hold my interest for long.
I'd skip the Ghost in the Shell movies and go straight to Stand Alone Complex. Not that the movies are particularly bad, per se, but they were among the first real cyberpunk things out there, so they spend a lot of time basically saying 'hey look, cyberpunk!' instead of devoting attention to characters and plotline like they should. SAC is awesome, but only if you like thinking and are in a rather alert mindset, because they absolutely refuse to simplify things or play down to the audience; don't bother watching if you can't or don't want to keep up.
Evangellion is a classic, beloved by many, and a huge influence on everything that came after it. I'm glad it happened, and I think that its existence has been positive for anime in general. But the show itself is kinda shit in my opinion. It starts out by deconstructing the usual unrealistic 'kid in a giant mecha' tropes, but then slides right into an even more unrealistic grimdark place. And of course the writer was gradually falling deeper into depression and growing to hate his fans as he went along, so a lot of it is deliberately intended to fuck with you. (Not gonna mention the ending)
While we're on Eva, might as well mention all the other 'oh I'm so grimdark and therefore mature and deep no really' shows. Gantz, Berzerk, etc. We get it, you're edgy and you show things a 'kids show' would never be allowed to. Adding Gorn doesn't make you mature, and tossing a bunch of rapists in your story doesn't make it deep.
Hellsing. The manga was a coherent story, centered on a girl adjusting to becoming a vampire in the middle of a supernatural war. The first anime tried to make it an episodic monster-of-the-week show centered on the God-Mode Sue side character who turned her and then acted as background for most of the series, only bringing back the real main character when they decide there needs to be a panty shot. Watch the Hellsing Ultimate OVAs instead; they're a faithful (and very well made) adaptation of the original story.
I would like to go on record to say that Star Driver, however, is not worth a look. I generally find these things being shown at my local anime club. How blissful it must be that I've forgotten half of what I didn't like in there and bought what I DID. Star Driver is one of those things that still cling to memory...badly.
Star Driver is the most stupidly ridiculously fabulous mecha anime there is. If you take it seriously you will hate it. It has a giant mecha with high heels and a giant feather plume coming out of its head, piloted by a hero whose prophetic title translates literally as 'Galactic Pretty-Boy', fighting against a "secret" society with a ludicrously inefficient lair, paper-thin disguises, and a membership which seems to include every person on the island who isn't in the high school drama club. If you are amused by the absurd, it's hilarious, but otherwise you should stay far away.
How about every yaoi anime ever? Most of the time it's overly dramatic soap operas with barely any interesting characters and highly inaccurate sex scenes; going in dry would hurt anyone, squeak.
I dunno, FREE! was pretty funny. But yeah, most yaoi is basically just shitty porn, like Queen's Blade for women.
Here, I'll throw in a recommendation too. Everyone should go watch My Teenage Romantic SNAFU. ignore how stupid the title is, It's surprisingly good.
Okay, I need to second this. I watched the first episode because I was bored at the beginning of the season. I don't know what I expected. The result was definitely better.
In that same vein, I recommend HENNEKO - The Hentai Prince and the Stony Cat. I have neither the time nor ability to explain why.