Right click in WMP when movie is playing -
Lyrics, captions and subtitles - On, if available.
If we are talking about non-DVD subtitles, Windows Media Player doesn't support playing SRT subtitles by default.
However, you can install DirectVobSub add-on.
More info.
Download
http://www.free-codecs.com/download/directvobsub.htm
May be this codec got corrupted on your computer, reinstall should help.