You can usually tell by looking at the packaging and/or the disc itself:

CD-DA discs a "Compact Disc Digital Audio" logo

CD-i discs a "Compact Disc Interactive" logo

CD+G discs the words "CD Graphics" (and perhaps even CD-EG "Extended Graphics")

PhotoCD discs "Kodak PhotoCD"

VideoCD discs a "Compact Disc Digital Video" logo and/or the words "VideoCD"

SVCD discs a "Super Video CD" logo (the words "Super Video" under the standard CD logo). The discs use one of the standard CD-ROM formats.

DVCD discs "DVCD"

HDCD (High Definition Compatible Digital) an "HDCD" logo. The discs appear to use the standard Red Book format.

SACD (Super Audio Compact Disc) is relatively new. The discs can have two layers, one of which is in Red Book audio format, the other in a DVD-like format offering higher fidelity.

DTS (Digital Theater Surround) CDs are just like normal CDs, but use DTS encoding instead of PCM.

VideoCD is different from CD-Video. It is an analog format, like LaserDisc, and the video can't be viewed with a CD-ROM drive.

There are a few references to Compact Disc MIDI (CD-MIDI).