The amount of trouble might depend on what sharing permissions you have set and what they might be downloading. If they're using your connection for downloading music/movies from P2P networks, you might wake up one day to a summons from the BPI for lots of cash. If you think someone's just hopping on to check their webmail, then you might be happy to do that. If you're on a limited bandwidth broadband service, you might also want to limit people's ability to use your account.
Do you have WPA or WEP security set up on it at the moment?
To stop your Airport Base broadcasting your SSID (which is the name of your network as it appears in your Airport bar in the menu bar), open up the Airport Admin Utility, select the network, choose configure and tick the box that says 'Create a closed network'. This will mean that anyone wanting to join your network would need to know both the name of the network and the password to be able to join it.
To filter the MAC addresses that can use your network, stay in the Admin Utility and click on Access Control. You'll see a + sign next to the box at the top, click on that and enter your Mac's MAC address (or Airport ID) and a description. Whenever any other computer/router wants to join your network, you'd have to go in there and update the Access Control list with the new MAC address. That includes things like Airport Expresses. You can find your MAC (Airport ID) in System Preferences, Network under the Airport tab of Configure or in the System Profiler under Network