I usually go for more balanced types in games, preferably melee balanced types. But occasionally I'll try for ranged. In most shooters and some RPGs I don't mind playing medic if the team needs one (sadly, most of the time they do).
Some MMORPGs that have more freedom with classes I like to do melee main class and ranged sub class to allow for close and far ranged options in combat like in Phantasy Star Online 2 with it's main class and sub class system.
I remember when playing Final Fantasy Explorers I went with the freelancer 'job' allowing you to basically build what you want. I liked being a damage dealer but also a healer. The healing wasn't as effective as a white mage's healing, but it's healing regardless.