Broadcast Live

Shows that are regularly broadcast directly as they happen, rather than prerecorded.

For the most part actually a few seconds behind, both for technical reasons (the signal only goes so fast) and legal ones (you need to be able to bleep things that offend the Moral Guardians)

If this only happens with select instances, it's a Live Episode.

Examples of Broadcast Live include:

Live Action TV

Saturday Night Live
The National Lottery Live
Ant and Dec's Saturday Night Takeaway
Big Brother Live
American Idol (and other countries' versions).
America's Got Talent (and other countries' versions).
So You Think You Can Dance.
What's My Line (Most of the CBS episodes)
Most early US Variety Shows, such as The Ed Sullivan Show.
Most news broadcasts; they might have taped/filmed segments but the anchor is usually live, and often the segments are too.
Most sports events.
The 40th Anniversary episode of Coronation Street
The remake of The Quatermass Experiment
WWE Monday Night Raw and WCW Monday Nitro
Late night talk shows (The Tonight Show et al) are generally broadcast live-to-tape; i.e., the show is recorded earlier in the day than its actual air time, but is brought to air without subsequent editing.
10 O'Clock Livea British news/satire show that, oddly enough, goes out at 10pm.

Film

The 2000 live broadcast of the remake of Fail Safe

Radio

The 1938 Orson Welles version of The War of the Worlds.