Texas Hold 'em is full of bad beats. It's part of the game. If bad beats didn't exist, then it would be an extremely boring sport.
A bad beat occurs when one hand that is statistically stronger than another ends off losing. A common example of a bad beat is when Player A has pocket Aces and Player B has pocket Twos, yet the river lands a third Two so that Player B wins the hand with trips.
Bad beats are also very popular to broadcast on television, because when the under dog wins, it makes the show less predictable.
When a player loses a bad beat, he often times goes on tilt, and becomes extremely emotionally. Psychologically speaking, it has damaged the player's ego. Some players aren't able to recover well from a bad beat. They may get up and leave the table for a while, or curse out the dealer, or begin to play more wreckless.
When a player begins to play more wreckless, it is important to capitalize on this behavior. The player may try to bluff more, in an attempt to steal pots and repair his ego. If you suspect this, you may consider pushing the player all in.
Below are some videos showing bad beats. In alot of cases, bad beats can knock you out of a tournament (as seen below) because you are so confident your cards are superior.
The video below shows multiple statistical anomalies in just one hand! First it shows a player making a statistically smart move (folding pocket Kings to pocket Aces) yet having a third King come on the flop. It also shows a player making a statistically poor move (going all in with pocket Queens) yet being rewarded with a Queen on the river.
Here's a classic, painful bad beat. Mabuchi is dealt pocket Aces with Phillips getting a King and Jack of Diamonds. The flop gives Mabuchi trip Aces and gives Phillips a gutshot straight draw. After the turn, Mabuchi has trip Aces still but his opponent gets his straight. The river comes and gives Mabuchi a fourth Ace, a fairly unbeatable hand. The only hand that can beat it is a Royal Flush, which his opponent gets, using that river Ace. It would have been downright impossible for Mabuchi to assume Phillips had the King and Jack of Diamonds.
This next one isn't a statistically shocking bad beat, but it's a very interesting one. It was televised during the World Series of Poker. Lovelace was dealt pocket Eights, while Mikkelsen put him all in with Ace King of Diamonds. At this point, Lovelace has a statistical edge, though Mikkelsen has many things going for him (2 over cards, connected and suited). The flop comes, giving Mikkelsen a Ten and Jack of Diamonds. The turn gives Mikkelsen the Flush, and the river gives him a Royal Flush. This hand just shows that anything can happen - as Lovelace went from a statistical advantage to being dominated.
A more disgusting example of a bad beat is below. Curtis, an amateur player, completely over bets with his pocket Aces. Farha, the professional, makes the call. At this point, Curtis has Farha dominated. The flop comes with three low cards, and one of them happens to be a Three. Farha wins the hand with his trip Threes. It is a stereotypical example of why many poker players hate pocket Aces.
A perfect example of a player going off tilt, Phil Hellmuth explodes after losing to Runner-Runner sevens. Hellmuth flopped top pair, yet Hoyt miraculously gets two Sevens to win the hand.