We'd like to hear detailed descriptions of problems viewing videos in standalone players and browsers. HTML5 and WebM especially are very new, and it's highly unlikely the experience in any browser is going to be free of hiccups quite yet. The more feedback we get about what doesn't work, the more we can do to make sure problems get fixed.
If you don't see your browser or player below, feel free to add it to the appropriate list. And to avoid any battles over natural pecking order, keep them in alphabetical order ;-)
A list of Ogg Theora players (without troubleshooting or discussion) with links to vendor pages can be found on the Theora Software Players page.
Firefox before Version 1.x,2.x,3.0.x
Firefox before version 3.5 (or 3.1 beta) did not include native support for Ogg or WebM. These broswers can play Ogg video via the Cortado applet if a Java runtime enviroment is installed. With Java installed, playback is seamless but does not have a full set of HTML5 features; resolution switching and chapter navigation are disabled. Cortado has native support for Ogg Kate subtitles.
Firefox 3.5 was the first version of Firefox to ship with native Ogg playback. It features a full HTML5 feature set, though it is known to be relatively slow about seeking and navigation.
Firefox 3.6 behaves similarly to FF3.5, but adds poster support and more robust Ogg stream navigation.
Firefox 4.0 (currently in beta)
Firefox 4.0 features a new Ogg playback engine that allows considerably faster stream navigation, as well as WebM support.
Google Chrome added Ogg playback support in version [?], but it known to have serious bugs when seeking in Ogg streams; it also tends to lose the beginning of videos. Recent releases of Chrome support WebM, which works considerably better, though the playback framerate is often choppy/jerky (at least on Linux).
Internet explorer 5, 6, 7, 8
Internet Explorer through version 8 has no support whatsoever for Ogg, WebM or the video tag. Normal installs do include Java support, however, so these browsers are able to play Ogg video through the Cortado applet. With Cortado, playback is seamless but does not have a full set of HTML5 features; resolution switching and chapter navigation are disabled. Cortado has native support for Ogg Kate subtitles.
Internet Explorer 9
Internet Explorer 9 (currently in alpha/beta) apparently at least somewhat supports the HTML 5 video tag, however it does not support Ogg playback and only supports WebM 'if the codec is installed on the system'. Presumably having the Open Codecs pack installed fufills this requirement and enables Ogg and WebM support (confimation would be appreciated!)
Internet Explorer 9 without Ogg/WebM support installed can presumably still play back Ogg video via the Cortado applet as in versions 8 and earlier (confimation would be appreciated!)
Opera long supported Ogg playback in developer builds, and finally shipped native Ogg support in release 10.5. As of 10.60, WebM is also natively supported.
Laugh if you must, but Navigator back to version 4 can play Ogg video via the Cortado applet.
Safari does not ship native support for Ogg or WebM video, however all versions can play Ogg video via the Cortado applet. With Cortado, playback is seamless but does not have a full set of HTML5 features; resolution switching and chapter navigation are disabled. Cortado has native support for Ogg Kate subtitles.
As of Safari 3.1, Safari supports full HTML5 Ogg video playback via the XiphQT Quicktime Components.
Standalone Players and Tools
FFMPEG / ffplay
As of release 0.6, ffmpeg supports WebM playback, and Ogg playback is solid with the exception of surround support (eg 5.1 and other surround encodings produced my modern Vorbis encoders will not play).
Prior to ffmpeg 0.6, WebM was not supported and Ogg video playback was broken due to a number of longstanding bugs caused by treating Theora as if it was just VP3 (eg, the 'sheet lightning acid trip' bug that caused the image to disintegrate into a shower of colored blocks). Many applications and video sharing sites (such as YouTube) are still using old versions of ffmpeg internally, and as such, they cannot handle Ogg video unless it is encoded in 'vp3 compatability mode'.
Media Player Classic
Mplayer has had a number of minor Ogg playback bugs in the past that mostly caused seeking or smoothness hiccups. Recent versions should have fixed all of the playback/seeking bugs of note. Mplayer can support WebM playback through libavcodec (ffmpeg libraries).