The anime industry has really taken a shit in the last 10 years with almost nothing of quality being released. A casual fan won't notice this since he'd be looking at the entirety of anime, but as some who's been a big fan since about 1979 I went from, "Dang, I haven't seen a good new show in a while." to "I'm starting to wonder if they even make decent anime anymore." to "New anime sucks ass".
Occasionally some good stuff comes out, but almost everything is either based on a Jump manga that regurgitates the Dragon Ball Z formula for the 100th time, or some sort of pederast school girl/maid bullshit. Things are bad, really bad. The two problems are 1) lack of money and 2) lack of talent. The two have been feeding off each other for a decade and a half and the result is that positions in the industry have been largely outsourced completely outside of Japan and the ones that still are in Japan pay very little. The producers will only approve tried and true concepts, so you get more and more of the same shit. Therefore making anime is no longer a respectable career, not even for otaku, since it pays nothing and only produces masturbatory shite.
However, good stuff still does manage to squeak through once in a while. The best thing I've seen recently is the new reboot of Mazinger Z. Since I've been a Mazinger kid for decades I can't really say how great this show would be for people who are new to the universe, but I was very very impressed. Its super hot blooded! Actual name: Shin Mazinger Shogeki! Z Hen. This is not to be confused with Mazinkaiser SKL, which was also cool, but way shorter and more abstract in an OVA sort of way. Shin Mazinger Shogeki! Z Hen the first all new TV length series with the old characters since the early 70s.
The best series I'm currently into is Gundam Unicorn. Its a 6 part OVA that will be released every 6 months until its done. If you like UC Gundam and have wondered what goes on after Char's Counterattack, you have to see this one.
Mainly my interests are 80s scifi and "adventure" anime like Gundam, Macross, Votoms, everything Miyazaki/Ghibli, ect. Things I would recommend to someone like myself grouped by release method:
TV: Votoms, Macross (OG), Macross 7, Macross F (maybe), Mospeada, Initial D, Yawara!, Touch, Nadia: The Secret of Bluewater, Z Gundam, Lupin III, Patlabor...honestly 80s TV anime is an almost inexhaustible well. I'm still finding awesome shit to watch.
OVA: Lupin III, Aim for the Top!: Gunbuster (I cannot recommend this one highly enough! Made by dudes who have read something besides manga in their life!), FLCL (pure rock and roll, I love it), Giant Robo (soooooo awesome. Best soundtrack of anything ever, amazing visuals, coolest f*cking characters I've ever seen), Angels Egg, Patlabor, To-y (hah, there's one nobody else here will suggest), Megazone 23 (all three parts, but mainly the first one), Birth, Dragon's Heaven.
Film: Macross: Do You Remember Love?, Patlabor 1 and 2, Robot Carnival, Mobile Suit Gundam: Char's Counterattack, Project A-Ko, Lupin III, Ghost in the Shell, The Wings of Honneamise (sometimes called The Royal Space Force).
Made for TV Movie: Lupin III (there is a new one every year, more or less), Crayon Shin-chan: The Parents Strike Back (soooo nostalgic and awesome/hilarious, best Shin-chan ever).
Things that deserve specific mention:
Run Melos: This was a direct to TV anime based on, I think, an early 20th century Japanese novel set in ancient greece. Its almost totally unknown and this is a shame because its one of the best things I've ever seen. If I had to sum it up on one word the word would be "trust". This is what I sometimes call "romance between straight guys" which is actually pretty common in asian movies (think: The Killer, 1989) but almost non-existant in the west for some reason. A man loves another man, but not sexually. Very hard to explain...
Ghost in the Shell: Stand Alone Complex: If you are into true hard scifi, not that Firefly bullshit, real scifi like 2001, Bladerunner, Solaris, Max Headroom, then you must see this. It addresses the inevitable conflicts that science and technology will bring to us in the coming decades like nothing else I've ever seen, and it does it episode after episode. Sadly the 2nd season really falls off, but the first is tremendous.