I spend a lot of time playing in the low-limit Stud games on Full Tilt Poker. In those games, I've encountered a number of players who haven't come to understand one of poker's fundamental concepts. These beginners focus only on their own cards; they don't stop to think about the cards their opponents might hold.
To take a typical example from Stud. I've seen players call with low and medium pairs after there has been a raise and a re-raise in front of them. These players are so fixated on their own cards that they don't stop to ask what hands they're likely up against. And in these spots, the betting tells a pretty disturbing tale. You can see how one player might raise with something like three high cards, so a pair of 5s or 7s could be best. But a re-raise? That's an indication of serious strength. At that point, a player should look at his pair and figure that, in all likelihood, he's up against a higher pair, making his smaller pair a big underdog. Folding is the only proper action.
A winning poker player won't just evaluate a situation at the start of the hand. He will constantly reassess as more information becomes available. Another example from Stud shows what I mean. Say a player raises on Third Street with the 4d as his up-card and I call with split 9s and a Jack kicker. We play heads-up and Fourth Street gives me a blank, the 5c, while my opponent catches the 8d, giving him two suited cards. He bets and I call. Then on Fifth, he catches another suited card, the Qd, and I make two pair with Jh. He bets again, representing the flush. Could he have caught the flush? It's possible. But in this case, when I try to determine what my opponent might have, I have to move beyond the cards that I'm currently seeing. I need to consider the actions throughout the hand.
I remember that on Third Street, the player raised with a 4 as his door card. Normally, players who are trying to draw to a flush will try to get in cheap on Third Street; they typically limp and then perhaps, call a raise. So while it's possible that this player started with something like Ad-Kd-4d, it's far more likely that he started with something like a middle or big pair in the hole. When I put all this information together, I see that despite the opponent's scary board, two pair is probably ahead, and I can react accordingly by either calling bets or raising.
This sort of thinking applies to all poker games. Moving beyond your own cards is a key step in coming to think like a winning player. The most sophisticated players in the game think a level deeper still - they consider not only what their opponents hold, but what their opponents think they hold. But that's the subject for another tip.