Please post some examples of...

when you have TPTK or TPGK and you get raised/check raised on the flop and how you play it. And discuss why you played it that way.

things to consider:
the more people that saw the flop, the more likely someone has a stronger hand. raises show alot of strength in multiway pots but not so much when headsup.

the exact pair you have makes a difference. TPTK with AK on Axx board is different from A9 on a 987 board.

what people think of you...do you have a good or bad image? if you have been playing tight and someone raises you (and you think they have some idea that you are tight) then use caution.

It's awfully dependent on

(1) Number of players involved as gabe indicated
(2) Board texture
(3) Read on player(s) (raise-calling range, how they play monster hands vs. draws vs. probe-minreraises, showdowns)
(4) your position
(5) your image at the table (depending on stakes anyway)
(6) Stack sizes
(7) Stakes
(8) Intuition

Probably a few other things I'm missing.

But it's hard to address as a general problem...I will say that at my stakes, most players will use a minreraise to indicate strength...2 pair+. A minority will use it for a draw - but that tends to happen mostly in small unraised (preflop) pots.
So depending on a lot of factors (my chances to improve to a hand that might beat them, reads, other players involved and their action, gut feel) I tend to call the first minreraise and try to put them on a hand based on the board texture and my read on the player. If I am oop, I will probably 50/50 bet vs. check the turn, assuming it's a blank. Bet vs. not has a lot to do with what I put them on (which comes from reads, experience, and board texture).
Sometimes I overthink things in these situations, and lose value ... but I don't tend to pay off all that many better hands either, so it's probably a wash as far as that goes.