Are health potions useful, or just white trash?

In previous Diablo games, health and mana potions were a staple of the game experience - you always wanted at least a couple of stacks of both, and they were generally bound to hotkeys or somesuch for easy consumption.

In Diablo 3, though, they're far more limited. Mana potions don't even exist, and there's a long cooldown between health potion uses. Generally if I'm in deep enough to need one, death is right around the corner regardless. I find myself selling stacks of the "old" potions to vendors periodically, for very little in the way of profit.

Should I bother picking up health potions? Are there situations where I will find them very useful, perhaps at higher difficulties? Or should I leave them lying on the floor, like so much other gray and white trash?

There is no reason not to pick up heath potions. At worst, a stack of 100 takes up one inventory slot. At best, they are essentially a free healing spell with a 30 second cooldown. Any little bit of healing can save your life.

Now, you definitely want to make sure you are always using the best health potion you can get. If you are out of type, another type is not used instead. You need to manually switch to them.

As a monk who likes to get right in the heart of the action, I find myself victim to a lot of spike damage. Enemies will hit me hard, but are unable to maintain their attacks before their demise. I can't spam my healing abilities, and sometimes I don't have the mana to do so anyway. Health potions provide just the boost I need to keep on punching.

They are definitely useful, although the level of utility depends on your class, skill/rune build, and the level of difficulty you are on.

In Normal, I found them to be largely useless. I think I used 4 potions before Act IV.

However, as the difficulty increases, the need for supplemental healing does, as well.

Particularly against bosses, uniques, and champion packs, the game generally rewards you for hammering on the baddies by spitting out well-timed healing globes to keep you going.

However, sometimes surviving until the next healing globe is a bit of a challenge, particularly for some of the less pleasant affix combinations. Healing potions can give you just enough health to get you to that next healing globe, which, in turn, will get you to the end of the fight.

Some escape abilities will help you prolong these tough fights, as well, allowing you to get several healing potions in over the course of the battle. As a Witch Doctor, I sometimes find myself popping a healing potion, dropping a DoT, then using Spirit Walk to buy myself some distance, nuking/dotting while kiting until my cool downs expire, at which point I can pop another healing potion.

It's not every fight (at least it shouldn't be), but they absolutely come in handy for particularly tough battles. Even if they only save your life once an hour or two of playing, it absolutely merits picking them up and carrying them. After all, they take up so very little room, and they don't sell very well. Just remember to upgrade them to the best you can carry, and don't make the mistake I did of forgetting to put the newest ones on the hotkey when you upgrade!