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).