Favourite type...hmm, that's a tough one. I usually tend to prefer certain pok?mon rather than certain types, I'm afraid I can provide you with no less than three favourites;
Ghost; Immune to both Fighting and Normal attacks and only two weaknesses, plus a lot of them are really strong and they learn sneaky moves like Will-O-Wisp, Spite, and Pain Split which I love to torment my opponents with. ^^ Besides, they're really cute, particularly Haunter and Banette (It's kind of ironic actually, I used to think Banette was scary XD).
Bug; A hugely underestimated type. A lot of them have a great deal of potential, take Shuckle for instance, enough defenses to make a grown sweeper cry in frustration. Another thing I like about Bug types is that most of them (Heracross and Scizor being perhaps two exceptions) require a good, working strategy in battle. Shuckle is of course my all time favourite of these, but I've recently begun liking Yanma and Forretress too.
Dark: I loved this type ever since I spotted that irresistable immunity to psychic attacks during my first playthrough in Silver. As we all know, psychic types, particularly Mewtwo Alakazam, held an unquestionably dominant position in the R/B/Y games. It was just too much fun when I fought against Arty and his oh-so-powerfull level 78 Alakazam in a link battle and it turned out that it couldn't do anything to my little Houndour. XD Besides, there are a lot of cool pok?mon in this type, like Houndoom, Umbreon, and Absol.
Overall, I tend to prefer the types that learn lots of moves for counter attacking or whittling away the opponent's strength rather than just straight out physical mashing (Fighting types I despise, *Spitts*), Grass (Leech Seed and lots of powders ^^), Water (Mirror Coats galore), and Steel (I looove that poison immunity, and that bunch of resistances rules too) are also types that I prefer. Nowadays, I tend to avoid using Fighting types (As I said, I despise them) and the same usually goes for Psychics, mostly because I'm sick of every second legendary pok?mon I run into being either fully or partly Psychic. <_< Come on, where's the Bug/Dragon legendary people? XD