There are many existing websites that will host your Theora content for free. You can then either link directly to the content from your own webpages, or refer people to the content hosted on the external site.
Archive.org (http://www.archive.org) is the website for the not-for-profit organization known as the Internet Archive, that focuses on the preservation of digital media. To post to the archive, you must also license the work under a Creative Commons (or similar) license. This is usually not a problem if you made the work yourself, but maybe an issue if you used copyrighted material (eg, music within a video) within your work, or if you are uploading something someone else made.
You can host Ogg Theora content at the Internet Archive for free, and then link to it from your own website. Archive.org will convert your video to Ogg Theora and many other formats when you upload it.
Note: when you visit a page on archive.org, it will notify you if your browser supports the video tag. If you see this message...
Simply reload the page and look for the message under the video icon:
At this point, click the link that says "try the new <video> tag" and click the following link to always use the video tag. Then your videos will display in Theora. If you'd like a direct link to the Theora version of the video, copy the "Ogg Video" link in the left sidebar. When you have that link, you can link directly to the video and anyone with a compatible browser will see the video play:
Dailymotion (http://dailymotion.com/) is one of the larger video sharing sites, and recently they have been dabbling with Theora support. They have converted over 300,000 videos to Theora, and by applying for a "motion maker" account (and getting approved) you can publish videos there using Theora. Their experimental Theora portal here: http://openvideo.dailymotion.com/. Note: not all videos in the portal currently display in Theora, so be sure to verify that your videos are working before relying on this service.
Wikimedia Commons ( http://commons.wikimedia.org/ ) is a website managed by the Wikimedia Foundation ( http://wikimediafoundation.org/ ), a non-for-profit organization that also manages Wikipedia. It is a database of media files available for anyone to use for any purpose. It's an open website that any can contribute to, which uses wiki software that allows for easy collaboration.
The site is managed entirely by volunteer editors, who also create the majority of its content by contributing their own work. The community is multilingual, with translators available for dozens of languages. It only collects material that is available under free content licenses or in the public domain. You can upload Ogg Theora files to Wikimedia Commons.