Embed locally hosted MP4 video?

Forgive me if this question betrays my own ignorance; I haven’t used this forum before. I have my own website on which I run WordPress. I’d like to stop using YouTube and start embedding videos that are hosted on my own website’s web space. Unfortunately, most of my videos are MP4 format and I would really rather not have to convert them all to something else (for example, I could convert them to flash videos and use a plugin I already have for that).

Is there an embedded video plugin that will let me embed a locally hosted file (NOT a video on an Internet video site) that is also an MP4? There’s one popular embedded video plugin that doesn’t support that file type, unfortunately, and I’ve not been able to find another on my own.