Wow this thread has become rather testy. The OP wanted to know if a general purpose grease at their local auto parts store was ok to use.

The short answer is yes, it's ok. The long answer is it depends on the grease and how tacky it is (because of the thickener and additives used and the greases stated/designed purpose) and what temperature range you want or the environmental conditions you will face in your local area.

It may surprise many that most "Bicycle Greases" are NGLI "2" greases, the same as automotive grease. Just look up Finish Line Teflon Bicycle grease (Here's a link to the specs - pdf) or Park's PolyLube 1000 Lubricant. To put into perspective, competitive in-line skaters and skateboarders use a NGLI "1.5" grade grease on their bearings.

I don't think anybody is going to buy a tub/tube of hi-temp disc brake grease or CV grease and use that on their bike bearings and it isn't designed for that purpose. Within the NGLI 2 spec, there is a relatively wide range of fluidity allowed. If one buys Slick 50's Grease One or Mobil One synthetic grease, you'll find those greases consistency and fluidity is closer to the minimum spec and seems more like a 1.5 rated grease because of the carrier oil and thickeners used.

The old DuPont Teflon Bearing Grease you used to see in bike shops has been replaced with Dupont's Krytox grease and I don't think many would buy a grease, even if it's considered the best money can buy, that's costs a minimum of $30 for a 2 oz tube of grease that's good from -95°C to +343°C and is slick regardless how thin the coating is, will stay there without shearing or washout, and not feel like it's dragging or holding you back because it's too tacky or thick. According to DuPont, Krytox has been used from the Mars Rover to Nascar and the Tour de France as well as precision miniature/micro machines and electronics. Although hard to find DTBG, you can still buy the old formula and it comes in an injector, Calhoun Cycle for example, and here's a picture of the packaging.

Most of these grease arguments are just over-thinking it. Even over at Bob's the Oil Guy forums, you'll see reps and techs from various companies argue for and defend their products over what is best for a particular application. The bottom line to to find a product, in this case grease, that meets your needs/satisfies the requirements while allowing you to get the maximum amount performance with the least effort from your bike and lasts/is durable.