How can I get the Mac Terminal to not beep?

In OS X Leopard (10.5 and later)

1. Open Terminal.
2. On the menu go to Terminal > Preferences.
3. Open Settings > Advanced ("Profiles" tab for Big Sur)
4. Un-check the "Audible Bell" option. (You can also set "visible bell" which will cause your terminal to flash instead of beep)

In OS X Tiger (10.4 and earlier):

1. Open Terminal.
2. On the menu go to Terminal > Window Settings.
3. In the Terminal Inspector window click on the drop-down list and select Emulation.
4. Un-check the "Audible Bell" option. (You can also set "visible bell" which will cause your terminal to flash instead of beep)

I'm presuming you have Leopard, whose terminal is greatly improved over Tiger's.

Terminal menu --> Preferences --> Settings tab --> Advanced --> Bell.

Untick "Audible bell"

(btw, mine doesn't beep as far as I can tell, even though that setting is enabled for me)

put "set bell-style visible" in your ~/.bashrc

The process is a bit different in El Capitan.

OS X El Capitan (10.11)

1. Open Terminal.
2. On the menu go to Terminal > Preferences.
3. Choose the Profile tab
4. Choose the profile from the left panel.
5. Un-check the Audible Bell option.

Steps after opening the preferences

On Big Sur (10.1)

1. open terminal app
2. On the menu go to Terminal > Preferences.
3. select Profiles (your profile should be highlighted)
4. select Advanced tab on far right
5. uncheck bell under Bell