This article is from the CD-Recordable FAQ, by Andy McFadden (email@example.com) with numerous contributions by others.
That depends on what was being recorded, how it was being recorded, and
how far along in the process things were.
If it failed while writing the lead-in, before any data was written, the
disc probably isn't usable. Some drives, notably certain Sony models, have
a "repair disc" option that forcefully closes the current session. This
would allow you to add extra data in a second session on the disc, but
anything written in the first session will be unavailable.
Failures when finalizing the disc may be correctable. Sometimes the TOC
gets written before the failure, and the disc can be used as-is. Sometimes
you can use a "finalize disc" option from a program menu that will do the
trick. Other times the recorder will refuse to deal with a
partially-finalized disc, and you're stuck.
Failures in the middle of writing result in a CD-ROM that probably isn't
worth trusting. Some of the data will be there, some won't. The directory
for the disc may show more files than are actually present, and you won't
know which are actually there until you try to read them.
Audio CDs recorded in disc-at-once mode are a special case. Because the
TOC is written up front, the disc is readable in a standard CD player even
if the write process doesn't finish. You will be able to play the tracks
up to the point where the recording failed.
If you were using a packet writing program like DirectCD, the experiences
of people on Usenet suggest that you are either 100% okay or 100% screwed.
The ScanDisk utility included with DirectCD 2.5 may help though.