I honestly can't decide on my favourites (mainly because I haven't watched much anime) but I would heartily recommend:
Shingeki no Kyoujin (Attack on Titan) - While I didn't enjoy it all that much, it is a very well made show with great animation in most places (still frames are more common than I'd like) and a pretty cool world. Also Hiroyuki Sawano's score is god damn fantastic to listen to. The man's a genius.
That being said, it's got some serious flaws that really killed my enjoyment, first, and most egregious of which being the pacing, which starts off a break neck pace for the first few episodes but slams on the brakes for the middle two arcs only to pick up in the last five episodes. It also suffers from the usual shonen problems such as an excess of melodrama, and episode padding in places. Deaths are also far to common place and for the most part the characters aren't really distinct enough for their deaths to hold any kind of weight. Add to that, the ending to the first season sucked ass. (Wait why am I recommending this?) But if you have a tolerance (as a good chunk of the internet seems to) for all that than you'll enjoy the show immensely.
Kill la Kill - It's an absolute blast to watch. The characters are great, not necessarily nuanced, but very likeable and fun to watch. The animation is great, especially the fight scenes, which are pretty balls-to-the-wall. The music is by Hiroyuki Sawano so expect eargasms to occur. It's got flaws, like the middle arc being way to long for what it was and the finale feeling like it could have used an episode or two more to get properly fleshed out, but even with those flaws, it's a very watchable show.
Tengen Toppa Gurren Lagann - This show. This fucking show. Very few shows I know of have started at its level of crazy and only gone further with it. Naturally, the show ends with one helluva bang (which I will NOT spoil and you would do well not to). Like with Kill la Kill, the characters are a blast to watch, albeit with slightly more nuance to them. Basically this show is the phrase 'Fuck yeah' given form.
Ghost in the Shell: Stand Alone Complex - Ghost in the Shell was a very smart film with a well realised and fleshed out world, interesting things to say on transhumanism and the human condition and some kickass action scenes to boot. That being said, it had some serious pacing issues due to its 80 minute runtime and need for both fast and slow moments. This left the plot feeling as though it skipped out some bit, leaving the final product significantly weaker. The show, on the other hand, doesn't suffer from such problems. Each of the two twenty-six episode series feels just as long as they need to be, a very rare quality for such shows. This is due to the very clever way they went about developing the main plots of each, with the series consisting largely of standalone stories with some link to the overarching story. This keeps the show overall as a slow burn, as a noir should have, while allowing each episode to largely do it's own thing, ranging from quiet character focussed episodes to brisk action to the odd quirky episode. It's a great show that you should not pass up.
Cowboy Bebop - Why haven't you watched Cowboy Bebop? Go watch it. There is no excuse. There's something for everyone. I would go on, but I'm really god damn tired.
