Are white or grey items worth picking up at all?

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?

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.

White and grey items are intentionally worthless, even according to Blizzard:

Bashiok: Diablo is about loot explosions. We can't realistically have loot explosions without a bunch of confetti and glitter that makes it all look exciting, but has no value except to make the explosions more satisfying. Gold still did this to a degree, but we were missing the "arrows and bolts" of yesteryear. White items were worth something and we really didn't have any junk we could just throw out with no limit. Now we do.

This was posted in response to concerns similar to yours, which came up because whites used to be worth something: you could salvage them into crafting materials, or convert them directly to gold (using character abilities in the beta, now removed).

Blizzard intentionally changed this, both to prevent the mentality that you needed to pick up every single item, and to add to the "loot explosion" idea Bashiok mentions.

Grey items are essentially useless and white items aren't much better. Their sell value is next to nothing, no more than 10 gold per item so it is not worth it very much to carry them back to sell.

Your inventory space is better occupied by blues which you can scavenge for crafting materials.

This also makes will make it feel less like you have to go back to town to sell things to empty your bags, whereas going back to town to scavenge an entire backpack of blues is much more rewarding.

The less time you spend travelling back to town the more time you have to push forward in the game and story.

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.