As aforementioned about a bazillion times, it really depends on the DM and campaign session. Sometimes, though, (especially in a difficult campaign), attacking what seems impossible may be a viable (or the only) option.
In one campaign, the DM's sole purpose was to try to kill the players off. We started in the middle of a desert with no food, water, and rudimentary supplies. Our characters were forced to drink half-coagulated blood from the carcasses of some bandits to survive (shifting us all a bit toward evil), and there was no holding back; nothing prevented the DM from unleashing something way over our heads.
One day, we were attacked by what can be described as a half-fiend penguin-bat. (Did I mention this campaign world was really screwed up?) It quickly tore through the low-level party, leaving most of them in the negative HPs, and turned to face my character. My PC was a level 1 druid with a Scythe (house rule allowed it), and I attacked it. I missed, and it brought me to 0 HP. Everyone else was practically dead, and my character was staggering his way to death.
It's a situation like that, despite its stupidity, attacking is pretty much the only alternative. I could have tried to get a Cure Light Wounds off on myself, but that would have only delayed death, really. Knowing it'd bring me to -1 HP and soon death, I took another swing.
Attack Roll: 20.
Roll to Confirm Critical: 20.
Roll to Assess Possibility for an Insta-Kill: 20.
Three 20's in a row. (That campaign had a house rule I often adopt where three 20's in a row is an insta-kill, unless it really really doesn't make any sense, e.g. a deity or somesuch. It tries to account for the fact that a pointy-thing in something's heart will kill it regardless of character levels.)
I sliced the penguin-thing in half, and promptly collapsed with -1 HP. Turned out that I made the stabalization rolls, and managed to get a Cure Light Wounds on myself before I died. The other characters stabalized, too, and a few Cure Light Wounds later, we were ready to go.
It's a great example of how much more rewarding a difficult challenge can be than a string of easy challenges.
THAT was experience well-earned.
-Mana
Edit: Fixed a few typos.