The more players that are involved in the hand, the lower your chances of winning the pot - even if you're a favourite. For example, the most powerful starting Hold'em hand is pocket aces. If you're up against a random hand, you'll be a huge 85% favourite. If you're up against five random hands, you'll still be a huge favourite, but you'll only win the pot 49% of the time.
On top of that, the more players in the pot, the higher the chances that they hold some of your outs. If two players have flush draws, they only have seven outs (not nine) to hit their flush and one of them might lose a big pot!