Playing from Behind on the Flop

[kingofswing]

I have a general question about play on the flop when you hit middle/bottom pair or have overcards. Let's say for simplicity there are three other callers and you who all just call an unraised pot. You're playing a hand with some value like Axs or maybe J9s and you hit, but not something you can feel comfortable with. If you don't have a big draw (like a pair and straight/flush draw), and someone bets out the pot what are the appropriate conditions for you to call to go ahead and try to hit an overcard or your kicker?

I know this is pretty vague, so let's say four caller to the flop and the following situations:

You have: Ac8c
Flop: Js8h6d

OR

You have: KsJs
Flop: 3s5dTc

Assuming the guy betting is an okay player what makes this hand playable? I almost always (like 99.9% of the time) lay this down without a second thought, but I was wondering if it's ever right to play hands like this? As a final consideration, how much does it matter if you could turn a flush or straight draw? Thanks.