A lot of good suggestions here. I agree with many choices while disagreeing others, but let me put forth more cogent list of recommendations. Not that the others are wrong, but because I wish to give some weight to my recommendations.
The following animes were all reviewed and then given rave reviews by mainstream critics, including not but exclusively, such as Ebert & Siskel, Ebert & Roper, New York Times, LA Times, Boston Globe, Seattle PI, Time, and others.
Akira, Jin-Roh, Princess Mononoke, and Metropolis.
Akira started the interest in anime and still remains a masterpiece of the medium. I'm sure you've all heard of it, so no real need to explain here. It suffices to say, whether you find it pretentious or not, that it is very highly thought of by critics, even those normally hostile towards anime.
Jin-Roh is a true cinematic tour de force--a modern masterpiece. A morality play that faithfully follows the Grimm brothers' Little Red Riding Hood, critics who've seen it have said that it best embodies both the possibilities and the limitations of the medium. It can do things with the palette, atmosphere that would be impossible with live-action, yet at the same time, the story suffers because the nuances of characterization needed for the two central characters are sadly found to be deficient vis-a-vis live actors. Jinroh is a character-driven story and needs something of Oscar-caliber performances from its main characters to complete it,w hich animation fails to deliver.
Princess Mononoke is another highly rated film; some critics have said that it was the best film of the year. It's probably the most Disneyesque of anime films you're likely to find, unless Disney decides to release more of Ghbli films. Others have explained it in previous threads, so just check it out.
Metropolis, I have not seen yet, but most critics gave it a high mark. Its main selling point seems to be its gorgeous imagery and visual brilliance.
I did not include Vampire Hunter D Bloodlust, Wicked City, Ghost in the Shell, or X because all of these films were critically panned. Out of these, X got the worst grade, followed closely by Vampire Hunter D.
It's unfortunate that the mainstream critics do not review anime series, as there are many worthy shows out there. I know that at least Ebert is very knowledgeable about anime, and I'm pretty sure there are few others who are familiar as well. Sadly, none, not even Ebert, has chosen to review them.
There is one instance of mainstream evaluation of anime series that I know of. Few years back, Time had a special on anime and did a number of capsule reviews on different series. Here are some that I remember as having positive reviews.
Ranma 1/2, the original Mobile Suit Gundam, Serial Experiments Lain, and... Can't remember if Tenchi or Sailor Moon got positive reviews, but I'm pretty sure that they were reviewed.