Not really easy for me to decide on my favourite anime ever, as I have quite a lot of favourites. But if I definately had to, it would have to be one of these:
→ Higurashi no Naku koro ni
Like Alter Ego said on his post above, Higurashi was able to mix cutesy with seriousness in an exceptional way. It also packed a whole cast of loveable characters and a great, immersive plot. After only a couple episodes, I got completely fascinated with the mysterious and instigating plot, and I definately wasn't disappointed to know it was much more complex than all of my theories. A great cast backed up with a great story- that's what all anime needs!
→ Princess Tutu
The only way I can describe Princess Tutu is "It's literally art". It merges animation, music and storytelling in a way that's so unique and superb I don't think I've seen any other form of media do it so well. I guess my adoration for this series comes from my fascination for both fairy tales and mahou shoujo anime, and how surprised I was to see both of them being so awesome together. It's also important to note that's one of the few anime I was actually rabid about my shippings, which shows how attached to the characters I was.
→ Dennou Coil
Dennou Coil is one of the few anime I've seen that never disappointed- every episode was satisfying, all important characters had their personalities developed and the plot always managed to have a twist surprising enough to make me bite my nails off every week while waiting for the next one. And not only the characters were developed, as was the whole world they presented us. Superb.