It took me a few minutes to think about it, but my all time top 5 favorites would be...
1. Spike Spiegel - Cowboy Bebop
There really isn't any other anime character like Spike. He has few fears, a very cool demeanor, an excellent sense of humor and sarcasm, but he's also laid back. He's a very deep person, his past haunts him. The way he views his past life, and his current life are very inspiring. I read he bases it off of a samurai/warrior code. His mannerisms and the way he presents himself are very neat too. On top of all that, he kicks major ass, and he's incredibly well voiced in the English version. (Steven Blum has a great voice.)
2. Ren - DearS
Ren isn't perfect, but I think that's what I love about her. She has flaws, considered a defective model in the anime & manga. But that gives her a very strong sense of humanity. She makes mistakes, and she doesn't do everything right. DearS are supposed to be perfect in almost every way from their abilities to their desires to serve their 'masters', the fact that she isn't and has some form of humanity intrigues me. Especially when she starts to accept human emotions and freely does things on her own. As this part of her grows, she becomes aware of things even though they aren't actually said. Furthermore, she has radical hair, and shes really beautiful too. Add super human abilities and some pretty hilarious comedic moments and you have a character you can relate with a bit more!
3. Dorothy Wayneright - Big O
Dorothy to me a very unique character. Although shes an android, as the series progresses she becomes more interested in things like emotions and general things about life. She has a passion for music, playing the piano no less which I myself do too every now and then. As well as having super human speed and strength, she adds a dark, very dry and witty sense of humor to Roger Smith's cool arrogance. The fact that she is a machine, but is curious about and may even be in love makes me love her. She learns a lot about human nature, including memories and feelings towards other people and animals during the series.
4. Vash the Stampede - Trigun
A very conflicted hero, Vash suffers more then most anime characters have in my opinion. Emotionally and physically he's been thrashed throughout the Trigun series, but all in all he doesn't change his unwavering views on life and how he should live it. He's a real dork most of the time, but when he has to fight he can do it really well. He loves donuts too, something I really like about him. He mixes comedy with deep emotion and action more then most protagonists I've seen. His choice of fashion is pretty cool too.
5. Chii - Chobits
Chii is freaking cute. Persocom or not, it's really sad how innocent and cute she is. It would seem like overkill but I can't really complain. Shes so bright and happy, but it's a very calm happy. Her nature leads to many comedic moments in the Chobits anime, acting casual, even nonchalant towards things that are perverted or wrong. She also discovers that she has feelings and emotions that a robot (or something not of the living I suppose) should not have. A big part of her character is finding ''the one for me'' and understanding all these complex feelings throughout the series and how she deals with them.
I would do 5 more if I could. I only have around 10 or possibly 11 characters I feel that strongly towards.