Since we're currently in a transition period, thanks to the lack of flash support on mobile devices and the introduction of HTML5, we have a few different common formats:
FLV: flash video format which was the most widely used for a few years, until the introduction of HTML5. This requires a flash-based media player.
H.264 MP4: (aka mpeg-4). This is a common video format which has a high compression ratio with a small filesize without destroying quality. Many flash video players support this format, and certain browsers support it through HTML5. However, the patents are owned by MPEG-LA, so this format is technically not free to use. As such, firefox offers absolutely no support for this format because of licensing issues.
Ogg Theora: Similar to H.264, but free and open source. This was mozilla's first choice as a competitor to H.264 to use as the default supported format in Firefox.
WebM: Google developed this, based on other open source formats. It was google's default supported format in Chrome.
Here's a table displaying which browsers and versions support which video formats for HTML5: [URL="http://en.wikipedia.org/wiki/HTML5_video#Table"]http://en.wikipedia.org/wiki/HTML5_video#Table
Currently, Ogg Theora and WebM are full supported in all the major browsers except IE. It should come as no surprise that once again, you have to treat IE differently. Also, Safari, doesn't support anything without a plugin.
So, the situation: the general landscape is moving toward HTML5 media players. While flash media players support all desktop browsers, they leave a number of mobile devices out in the cold. Since mobile is popular, that is potentially a large portion of your audience which won't be able to access your media content.
As for HTML5, supported by desktop and mobile browsers alike, there is the issue of the major browsers not supporting a single video format across the board. As such, most folks end up having two or three copies of the same video in different formats. Some example HTML:
<video width="640" height="480" controls> <source src="myvideo.mp4" type='video/mp4; codecs="avc1.42E01E, mp4a.40.2"'>
<source src="myvideo.webm" type='video/webm; codecs="vp8, vorbis"'>
<source src="myvideo.ogv" type='video/ogg; codecs="theora, vorbis"'>
So, the browser should be able to choose a supported format.
In addition to implementing HTML5 video tags, some folks also offer a fallback to flash video players if a browser is not HTML5-capable, and can still support flash. But--this pool is rapidly shrinking.
In order to determine what is best for your particular site, you will have to look at the browser analytics data of the visitors on your website.