One cool thing about Bitcoin is that coins are inherently scarse and this is by itself a huge protection from sybil attacks. In other P2P systems, sybil attacks are much harder to prevent because there's no such concept of scarcity. In Bitcoin, a sybil attack would be achieved if one has lot of coins, by sending tons of transactions, and therefore spending such coins.

There are other types of sybil attacks such as overloading nodes connections, and the recent one of filling up the memory pool of specific nodes with really tiny transactions. A way to prevent these would be for example to increase the fees.