Your TV has interference. Eavesdropping signals can interfere with TV broadcast frequencies, specifically UHF channels. You can even use a handheld TV with an antenna to sweep a room for interference.
You are the victim of a burglary, but nothing was stolen. That person who broke into your home or office may not have been after your precious possessions, but rather your conversations. If you've become the victim of a fake burglary, it would be wise to double-check your lines.
Your wall plates are moved. A wiretapper may use your phone's wall connection to gain access to your line. Look for signs that this hardware is a different color or crooked, and definitely take a closer look if you notice debris on the floor or screws that have been moved.
You've had a mysterious repair. Some wiretappers will gain access to your line under the guise of a repair. If a utility-company employee shows up when you haven't specifically requested one, there's a good reason to be suspicious. Call to verify the repairman's visit with your provider or watch his actions carefully.
There are no signs. If you don't notice any of the aforementioned signs, your line could be wiretapped anyway. Most amateur spies will exhibit at least one the telltale signs outlined above, but government tapping is executed at the local exchange-carrier-switching center of your phone company, so there are no strange sounds to hear or hardware to find. If you truly want to have a private conversation, do it face-to-face.