VideoLAN is an open source multi-platform video player that has built in support for H.264 (no additional software required).
This is the easiest way to playback H.264 encoded content, although it may have trouble with the AAC encoded audio. This method is listed at the top because this is the easiest to try (no need to mess with installing codecs, etc...).
Pro: Easy to try. No additional software required. Good compatibility of H.264 playback. Free.
Con: May not handle AAC audio well. Not the most efficient.
Download: VideoLAN Download Links
ffdshow (using Media Player Classic or Windows Media Player):
ffdshow is a Directshow filter that supports the decoding of many video and audio formats, including H.264 and AAC. With it installed, you will be able to use any Directshow capable player to playback H.264 videos, including Media Player Classic and Windows Media Player.
This method is slightly trickier, but should offer the best compatibility.
Pro: Very good compatibility. Works in many media players. Has AAC decoder. Free.
Con: Not the most efficient.
Instructions: H.264 playback using ffdshow + Media Player Classic (or Windows Media Player) playback instructions. If you don't mind using a codec pack, you can refer to these instructions instead.