Don't give them up, you will profit in the long term by playing 2 pair. As with all hands, except straight flush etc, expect to lose a small portion of the time.
If you hit 2 pair on the flop against 1 opponent, you have 85%chance to win. Against 2 opponents, 75% chance. Against 3, 66% chance.
Sounds good, yea? This is assuming you didn't start with a pocket pair and another pair hit the flop - you were dealt, for example, 10,9o and the flop was 10,9,A.
-edit- in case you were dealt a pocket pair and another pair hit the flop, you still have good chances of winning as there is only 1 other card for them to pair with, and the chances of making a set is something like 2.2%. Just be careful that the other card is not higher than your pocket pairs.
2pair it depends on the flop. really, is there a flush/straight that can beat you ,do you have the best 2pair do you have the second best 2pair. most of the time, you have the apponent beat with 2pair, But you should look at how many chances there are that the apponent has you beat