XD, lets see...
Furi Kuri- Very well recieved series. Winner of Best Comedy and Best Short series at the American Anime Awards. 3rd place at the Fantasia film festival.
Ghost In The Shell- Argueably the greatest cyber-punk series of all time. Another very well recieved series that has some of the greatest cultural influences of any anime in exhistence. In the US for example, I have seen the manga used as a required college reading. Not only that, American MOVIES have been influenced by this series. Most noteably the director of the Matrix admitted that his movie was influenced by Ghost In The Shell, and it you can see many similarities between the two.
The first movie alone was winner of Best Screenplay at the Yokohama Film Festival, Best Feature Film and Best Director at the World Anime Celebration, and the International Film Fantasy Award.
Mobile Suit Gundam Seed- Part of the longest running mecha, and has more installments out than any other anime series ever created.
Serial Experiments Lain- The defacto psychological/horror series, essentially defining a new genre of anime. Winner of the Excellence Prize.
Shakugan no Shana- People are somewhat obsessed over the red headed tsundere loli. Of course, I actualy kind of agree with you on this one.
The Melancholy of Haruhi Suzumiya- At the time it aired, it was the most popular television show in Japan for 18-34 year olds. Constanly makes top 10 anime lists (number 4 all time series in a recent poll in Japan). The followers have formed their own religion called Haruhiism. Won the Animation Kobe Award for TV Feature, Best TV Anime Series and a voice actor award at the Tokyo Anime Awards.
Yep, I think men in black suits will be coming after you shortly. Of course, I may get crucified for some of the series that I list, too.