I burned a DVD in my computer, why won't it play in my DVD player?

This can be caused by many different things as there are many media formats and recording formats for DVDs. Even if you used a DVD authoring software to create and burn a DVD movie compilation to a DVD-R disc, it still may not play in all players. This is especially true with older or basic DVD players.

There are three competing DVD media format standards, DVD-R/W and DVD+R/W have pretty similar features and are compatible with many standalone DVD Players and most DVD-ROMs while DVD-RAM has less DVD Player and DVD-ROM compatibility but better recording features.

DVD-R and DVD-RW

DVD-R/W was the first DVD recording format released that was compatible with standalone DVD Players.
DVD-R is a non-rewriteable format and it is compatible with about 92% of all DVD Players and most DVD-ROMs.
DVD-RW is a rewriteable format and it is compatible with about 75% of all DVD Players and most DVD-ROMs.
DVD-R/W supports single side 4.7 GB* DVDs (called DVD-5) and double side 9.4 GB* DVDs (called DVD-7).

DVD+R and DVD+RW

DVD+R/W has some "better" features than DVD-R/W such as lossless linking and both CAV and CLV writing.
DVD+R is a non-rewritable format and it is compatible with about 86% of all DVD Players and most DVD-ROMs.
DVD+RW is a rewritable format and is compatible with about 75% of all DVD Players and most DVD-ROMs.
DVD+R/W supports single side 4.7 GB* DVDs (called DVD-5) and double side 9.4 GB* DVDs (called DVD-7).

DVD-RAM (Not a PC media format)

DVD-RAM has the best recording features but it is not compatible with most DVD-ROM drives and DVD-Video players. Think more of it as a removable hard disk. DVD-RAM is usually used in some DVD Recorders.

Other non-standard special DVD recording formats:

DVD-VCD is basically a VCD (Video Compact Disk, normally written to a standard CD) authored on a DVDR/W. DVD supports the VCD resolution but the audio has to be resampled to 48khz.
DVD-SVCD is basically a SVCD (SuperVideo Compact Disk, normally written to a standard CD) authored on a DVDR/W. DVD does not support the SVCD resolution but it may work anyway and the audio has to be resampled to 48khz like the DVD-VCD.