Question: Once you're past the first few levels and not desperate for any little bump you can get, is it at all worth picking up the whites and greys littering the average battlefield?

I'm know that every penny counts but would you make more by pushing forward and slaying gold dropping foes or getting to Nightmare and seeing more blues?

Answer: 
In general, I completely ignore whites and grays - typically they're worth less than 10 gold a piece, which is not even worth dragging back to town. **Do note** that some "special" objects such as health potions and gems have white text, which might be confusing if you're completely ignoring that font color categorically. 

In the very early going, when you have equipment slots that are completely empty, they're worth grabbing just so you're not *completely naked*. In particular, when you're just starting out, keep an eye out for a Targe shield - it's got typically around 50 defense, which outclasses most of the defense you'll find on any other item at this stage of the game. 

In the very early phase of the game, you can occasionally find a white weapon/armor piece that has slightly better DPS than your current weapon - I've found white weapons better than blues I had from previous dungeons in the early levels previously. For this reason, sometimes I'll grab (or do a quick check by hovering over it and pressing CTRL, as bwarner notes) the first white item of a type I find, just to see if it's a class better than my current gear.

Past about level 5 or so, though, you're better off leaving them where they drop. Once you have items that give you beneficial stat boosts beyond the basic defense/DPS rating of the item, whites and grays are almost always going to be worthless to you. Even if you can get a few extra DPS or defense points out of a "higher tier" white, it probably won't offset the utility of the other bonuses on your current gear.
They're practically worthless. The amount of money you make by picking up an entire inventory of whites and greys and selling them can easily be made by pickung up one blue and selling it.

They also don't get you more money in higher difficulties, at all.