Yeah, there are still good anime out there, but the early 2000s was really the end of there constantly being quite a few good anime out every season. In the past five years, instead of "hey, what was good in the fall or spring?" I have to ask "hey, is there any anime from 20xx worth a fuck?" The anime industry has been catering to the otaku too much. Most otaku have the same taste in anime that they had when they were younger, but at 22 years old, I don't want to see an anime full of fanservice where the girls look like they're 12.
You are deluding yourself either with nostalgia or the fact that in the early 2000s most people weren't directly following the release seasons in Japan (it was the anime boom when lots of companies were going back to license old works so releases were covering many years at once). As Mickeymac said there are lot's of good shows today and there really weren't any more good shows in the past. Don't forget Sturgeon's Law - 90% of everything is crap. But there's still that other 10%.
If you want to know what's good in a particular season you do have to actually put some effort in, but that's always been true. Here are some examples:
Current Season: I would recommend Kokoro Connect and Sword Art Online, though it has admittedly been a weak season.
Spring 2012: Fate/Zero, Kids on the Slope, and Nyaruko-san were all great (and all very different).
Winter 2012: Natsume Yuujinchou Shi, Another, Ano Natsu de Matteru
Fall 2011: Fate/Zero (first half), Bakuman S2, Chihayafuru
Need I go on? I've also been watching Sket Dance this whole time (it's the only long show I follow anymore, being a pure comedy avoids the ridiculously-drawn-out-fight problem). Not a single show I listed is particularly fanservicey, and the only one that's really fits the otaku stereotype is Nyaruko, but it's a comedy that's not afraid to poke some fun at it's own audience.
I seriously have to wonder if people claiming that there's no anime worth watching have actually looked...