The complications start when you start claiming them. Once a fork is launched, you're likely to find a lot of wallets, in which you will need to import your Bitcoin private key to gain a corresponding amount of the forked coin. Fake wallets are going to take your private key, and steal any Bitcoins within. Make sure you only use the official wallet for the fork and empty the Bitcoin address whose private key you will import beforehand.
This is extremely important. The danger comes from a thief replaying the transaction you made on the new chain. If he replays it on the original Bitcoin chain, then he can claim the coins in the transaction from your Bitcoin wallet. If the wallet is empty, then he can't do this.