These three hands are fairly low-content (and obviously brags about how awesome the games I play in are), but they illustrate the importance of not slowplaying your monster hands. (The only exception is when the effective stack size is very short, or your opponent is just a ridiculously spewy three barreller when checked to.) It's really important to play monsters similar to how you would most of the rest of your range. Checking them so that you can raise later is very transparent and misses opportunities to build the pot against players who call very liberally.
Hand 1 (NLHE 2/5): Hero has $800, villain about $650 to start the hand.
Villain opens to $20 in MP, loosey goosey fish calls $20 in the CO, and I raise to $80 with Q Q . Both players call, making the pot about $240.
Flop comes Q A Q . Both players check and I bet $65. Here's my thinking for bet sizing: I expect every Ax hand to call this size bet as well as future bets on later streets. I also think broadway gutshots will peel here and small pairs might as well. Villain goes all-in, loosey goosey folds, I snap. Villain flashed her hand to someone else across the table and I think I heard her say that she had AK. What she was doing going all-in, I have no idea. She may well have gone broke anyway in this hand had I checked the flop, but the flop bet was mostly to try to get value from worse hands.
Hand 2 (NLHE 2/5): I have about $1200, villain has me covered.
Villains opens to $25 in the CO, I call in the SB with 9 9 . We go heads up to a flop of 4 9 4 . I check, villain bets $35, and I raise to $100. Villain folds. (Oh well, can't stack them every time . )
Before the final hand, some relevant history on villain. When he thinks he has the best hand, he (over)plays it very hard. Example: Opponent raises to $40 in a straddle pot in late position, and villain makes it $140 in one of the blinds, only the opponent calls. Villain bets $300 on a flop of T 7 5. Opponent calls. Turn is the A . Villain checks, opponent bets $600, villain thinks for about 2 minutes, then decides he is all-in for $800 more on top. Villain calls. River is the K and somehow villain wins with J J . LOL.
Hand 3 (NLHE 2/5): Hero has $1900 to start the hand, villain covers (see above). Two limpers in a straddled pot, and I raise to $50 with J J. Villain calls on the button, the straddler calls and the two limpers call, so the pot is about $250 before the flop.
Flop comes 2 2 J . Checked to me and I bet $100, villain raises $200 more, everyone folds back to me, I reraise $350 additional, villain raises $1150 more, I go all-in for about $50 more, he calls. I assume that I coolered his A2s until he reveals that it was a "bad beat" because he had AJ and he couldn't put me on the last two jacks in the deck. The lolcano exploded and I went for a ride in the roflcopter (in my inside voice).
For the last hand, I think my initial flop bet-sizing ensures that 2x gets it in, gives a good price for flush draws and small pairs to continue in the hand, and also gives someone a chance to make a spazz bluff or what have you. The 3bet gives a price that I know the opponent will at least call if he has a flush draw, while ensuring that the money continues to go in if he has a hand he wants to go with.
Of course, I definitely appreciate any criticism if you all find flaws in my reasoning. But overall, I would summarize live poker as "give people a chance to make huge mistakes when you have a strong hand" and betting (even if your sizing isn't huge) accomplishes that a lot better than checking.