I've always prefered the all-rounder type of character regardless of genre. So in a Supers game I'd be trying to put together someone who could fly, zap, and have another power or two just in case. (A bit of Invulnerability or Damage Reduction wouldn't hurt!

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That's my preference as well. I prefer for my super-heroes to have some sort of offensive ability, some sort of defensive ability, a means of getting around and some random utility power (super-senses, self-healing, whatever).
Some of my favorites include;
Firedrake looks like an older man, but is far older than he looks, as he's part dragon, able to transform into a nine foot tall, scale-armored, winged, clawed and fire-breathing dragon-man hybrid. In addition to my standards of decent attacks (strong with claws, fire breath) and decent defense (thick scales provide armor like protection) and self-transportation (winged flight), he's also got superhuman senses and heals what a human would heal daily on an hourly basis.
Kensai, the Angel of Blades a mute swords-mistress made of steel. She's tougher, stronger and faster than human (and surprisingly stealthy, for a woman made of shiny metal), and able to create blades of steel (from daggers that she throws, to swords that she wields) with a thought. With concentration, she can slice a rift in space to allow her limited teleportation.
Impact looks like Sebastian Shaw, the Black King, complete with the freaky Victorian outfit. Has the same powers, as well, absorbing kinetic impact and using it to boost his own strength and (to a limited extent) speed. Acts more like swashbuckling Nightcrawler or Fandral of the Warriors Three, complete with a fencing saber. His kinetic energy absorbtion provides him with a good defense, decent offense, and using the energy to increase his running speed, or to power a super-jump, it's a halfway-decent means of transportation.
Totem Native American who has the abilities of various animals native to the pacific northwest. Strong as a bull, fast as a snake, able to fly like an eagle, swim like a fish, deliver a venomous strike like a rattlesnake, etc. Can speak with animals and while not capable of full blown animal control, can suggest courses of action to them. Lots of enhanced senses and minor powers, but is saving his experience to take on the strength of the totem animal he is currently communiing with, the whale. Basically a North American version of Vixen, but limited to animals that his ancestors interacted with. (No cheetah-speed or elephant-strength, for instance.)
Some characters I've toyed with for;
Aberrant
GURPS Supers and
Mutants & Masterminds
I've also got at least a hundred V&V characters lying around (and nearly a hundred CoH, CoV, Champions Online and DCU Online characters), but they never it made it onto my website.
I love designing superheroes.