You can't do anything with an address, but send coins to it.
That's not true. The other thing you can do with an address is see all transactions to and from that address. The worst that can happen is that someone could use this information to determine who you are, who's paying you, what they're paying you for, and what you're spending your money on. To help protect your privacy, it is recommended that you generate a new address each time you wish to receive coins from someone, and don't reuse the same address for multiple payments or publicly post your addresses unless you're aware of the privacy implications.