Man, just about *every* skill is needed, but, I'm an admited skill junkie. Skills that you *have* to have are a combat skill, a back-up combat skill, sneaking, etiquette, and perception, but man, there are so many afte rthat that are still vital.
4 dice in a skill is a darn handy number, serving as a nice bit of emergency back-up. (This doesn't apply to Demolitions, however. Eithe rlearn it a lot or not at all, learning it a little's just bad for everybody, ol' Eddie Eightfingers.)
So, with a 3 Logic or 2 Charisma, I want 1-2 in a bunch of skills to at least get by in life, plus a few for my strengths as well.
For instance, Athletics Group 1-2 gives you basic competency in things like swimming, climbing a fence, or outrunning the cops, all important, but not the kinds of things where you need 5-8 in it.
Unarmed Combat is a nice backup for anyone... you never know when you'll have to go someplace where you just can't sneak your gear in.
Throwing Weapons 1-2 is enough to get a grenade where it needs to be. Defaulting with your untrained self and Agility 3 is a good way to make your (surviving!) team members hate you.
Pilot Ground Craft 1-2 is one of those things that everyone needs. Nobody wants to be the 'runner on a bus.
Con of 1-2 will get you past problems, as will Intimidation, and there's just no excuse for not having enough Negotiation to buy the stuff you need. 4 dice for shopping will at least get you ammo without having to overpay. Those Cha 1 Street Sams with no Negotiation ... man. Having to beg people to shop for you has to be hard when you have 0 dice for begging.

Disguise helps get you around cameras (Or, more precisely, helps you not care about them), and Navigation tells you where shortcuts are and how to get to obscure places where GPS doesn't go ... like teh Barrens.
Surely you've at least a smattering in a second language, right? RIght?
A little First Aid goes a LONG way, while 1-2 in Cybertechnology and a kit lets the Street Sam keep his bits in working order for routine needs. You hate to drop a hundred nuyen to see yoru Cyberdoc every time you need your fingers tightened after all. Speaking of which, if you shoot things a lot, you should reallly have a point or two in Armorer, to help you service your weapons.
It never hurts to have a mechanic around who can keep your bike running, but an indutrial one who knows what those buttons do? Priceless.
1-2 in Electronic Warfare will help you do comm operations well, deal with jamming to a degree, and let you watch a few broadcasts for free when you have downtime.
Lastly, everybody needs to have 4 dice in COmputer, just to survive the modern world. Those things are *everywhere*. Really sucks when you go to give CLyde a 50 Nuyen bribe at the bar and wind up tossing him 5K instead, you know?