Usually I do my Dwarves some variation of scottish when I'm thinking about it.
Mostly, though, I realize that I'm not a gifted method actor, and I usually GM, so I tend to take a more narrativist tone with third-personisms and the occasional booming "Announcer Voice" and a 'When we last left our intrepid heroes ...'.
My current character I visualize as played by Patrick Warburton, but unfortunately I just never could "get" him. He's sort of, personality-wise, if The Tick were a champion for The Christian Right.
My replacement PC I decided to go for something I COULD do ... silly French "Holy Grail" accents! Jean-Claude Phillipe Baptiste D'Argent, a Dragonwrought Kobold raised by a French-Canadian ... er ... Furyondish couple.
The group I play with now, they've moved the various D&D languages into silly accents ... Celestial is French, Terran is Russian, and our two Hill Dwarves sound like they're out of a Greyhawk production of O Brother Where Art Thou?.