A Typical Scenario .......
You are sitting in the big blind with 

there are 4 limpers and the button raises. The small blind calls and it is back to you. There are 9 small bets in the pot and 4 limpers still to act, who will probably (correctly) call. Your (current) pot odds are 9-1, and even though you have poor position, your current pot odds, plus the implied pot odds make it worth a call - you are probably no worse than 7-1 to win this hand.
You call. The 4 limpers call and the flop comes:
there are 4 limpers and the big blind raises. The small blind calls and it is back to you



At this stage, assuming the raiser has some decent hand you expect to have something like a 10-15% chance of winning the hand
It is checked to you. You have nothing worth betting and with 5 people still to act there is no realistic possibility of stealing the pot. A check is the right call.
At this stage, assuming the raiser has some decent hand you expect to have something like a 10-15% chance of winning the hand. Very little I know, but look at the odds the pot is laying you! Because of your position and your chances of winning the hand, there is no point in raising, so you simply check along.
The first limper bets and the second limper raises. The third limper folds and the fourth limper cold-calls, as does the pre-flop raiser.. The small blind calls and it is back to you. The pot is now 19 small bets, and it costs you 2 small bets to call.
Now lets consider where we are. We are in a 6 way pot, in early position. We have an Ace-rag hand, and the button (pre-flop) and the player to our left (post flop) have showed some aggression. We are almost certainly losing at this stage.
So, an automatic fold? - Not on your Nelly!
We are a major (under-)dog in this hand - maybe a 12% chance of ending up with the best hand, with awful position,
But!
We have great pot odds. We are getting 9.5-1 to call (10.5 in decimal terms!), and better if we consider the implied odds (i.e. what we can expect to make when we do hit our hand).
We call, and the original bettor calls behind us.
The turn comes - 
The small blind checks to you. We should check, right? I mean, we have nothing? Not necessarily! Consider where we are, and how our opponents will perceive us.
At the moment there are 11 big bets in the pot. We have 4 players (and the small blind, if there is a bet) to act. The first limper bet into the pot on the flop, indicating he had something - but chose not to re-raise.
Very simplistically we should only bet if we have positive equity in the pot, ie. we are more likely to win than the odds the pot is laying us
He, we can assume, has a good, but vulnerable hand.
The second limper also obviously has something he liked as he cold-called a raise on the flop, and there is also the pre-flop raiser. All of these players are likely to stay in the hand. So the question is, should we check or bet? Very simplistically we should only bet if we have positive equity in the pot, ie. we are more likely to win than the odds the pot is laying us.
If we do bet in such a circumstance, in the long run, we will make money. So, we need to evaluate our holding. We have an overcard to the board, and no reason to believe that a pair of Aces won't win the hand. Additionally, we have a draw to the nut flush, and a draw to a gutshot straight. Any one of 9 clubs will give us a cinch hand (although the
could potentially make someone a full house or poker). Any 4 will also lock in the hand for us, although we must remember not to double count the
. We could also potentially win by spiking an ace, although we can't be sure of that (a pair of Aces) being sufficient. Overall, we have 9 clubs, and 4 fours, slightly discounted, plus the possibility of an ace winning us the hand On balance we probaly have about 13-14 outs with 46 cards to come.
That means anything over about 2.5 to 1, make a call worthwhile. So we know we are staying in this hand, but should we bet? The answer is that we should bet if we have equity in the pot.
At the moment the pot is laying us 11-1, and we have a greater chance than that of winning the hand, so we should bet. The bet is doubly beneficial as it is likely to confuse out opponents, and a raise won't really hurt us. We are at worst here a 4-1 underdog, and even allowing for the poor position, we have equity. We should bet!
We bet, and all 5 players call. The pot is now 16 big bets.
The river comes:
and the small blind checks to us.
We have made our flush and we have to decide whether to check or to bet. Many players would check here - fearing the fact that the board has paired. That would be a very bad mistake! Should anyone have a pocket pair giving them trips on the last round (i.e. they held KK, 33, 55 or 66) they would simply have to have capped the betting to chase out any flush draws on the turn - where they were overwhelming favourites.
Furthermore we can probably rule out KK - while the buttons raise pre-flop is consistent with such a holding, the fact that he chose not to re-raise on the flop makes it unlikely. The player we need be more concerned about is limper who raised on the flop. That play is quite consistent with a low pocket paid such as 55 or 66.
So we should check to this potential monster then, and make a crying call - right? Wrong!
There are 16 big bets in the pot. That means that we only need less than a 6% chance of winning
the hand to call a bet here - i.e. we are going to have to call any single bet. Even a double bet will be laying us 8-1 or more, and we have the nut flush!
Similarly, all the other players are getting the odds to call - even if they feel they are probably beaten. We should take the initiative here and bet!
The four most likely scenarios are:
- We check and everyone else checks behind us - it is quite common to see such timid play at low-limit tables
- We check and someone behind us bets
- We bet and everyone else behind us calls
- We bet and someone behind us raises
The moral of the story is - before you fold a rag hand, think about the pot odds...
The first scenario will see us lose potential profit when we have the best hand. In the second scenario we are going to call anyway, so we might as well bet.
Not that a check might be correct against a single player in a smaller pot - as we are only likely to be called if we are beaten. Here we will be called anyway because of the size of the pot by betting we ensure that all the players put more money into the pot.
The third scenario is what we are trying to achieve, while even the fourth scenario is not a disaster - it is possible that a tricky player may want to define his hand, or even try for the pot with the second nut flush.
So the moral of the story is - before you fold a rag hand, think about the pot odds and the chance you have of back-dooring the winning hand. However, please don't read this as a license to play poor hands (which A7 offsuit is) from early position. There are very specific factors here related to the number of players in the pot, the pot odds and the the presence of back-door outs that make it worthwhile.
Rather, what you need to take from this, is that there are times where it is right to call, or even bet and raise, when you are fairly sure you have the worst hand - you just need enough chance to win more often than the pot is laying you. In certain circumstances - namely multi-player pots where you can close the betting with great pot odds, it can be worth staying involved!