As an alternative to downloading the whole XML or SQL data dump, it's nowadays possible to use SEDE to find and download all your posts, and only your posts.
Here's a query I just wrote that returns the Markdown and HTML content of all posts by a given user, plus a bunch of other useful data (including a list of all user who have edited the post, to help with providing attribution for posts with multiple contributors).
To use it, just select the SE site you want to download your posts from (using the slightly awkward SEDE site selector), fill in your numeric user ID (as found in the URL of your user page on the selected site) and click "Run Query". Then click the "Download CSV" link and import the resulting CSV file into whatever program or database you like (or just save it as is).
(Trying to open the CSV file e.g. in Excel doesn't really seem to work properly, presumably because all the HTML and Markdown text in it confuses Excel's CSV parser. But Python's
csv module, for example, parses it just fine.)
Of course, you can also use the query to peek at someone else's contributions. For example, here are all my posts to meta.SE.
(Alas, it looks like trying to fetch all of Jon Skeet's posts to SO times out. I may need to optimize the query further.)
Update: I made a cross-site version of the query that returns all your posts on all Stack Exchange sites.
To use it, you need to enter your Stack Exchange network account ID, which you can find by going to https://stackexchange.com/ and clicking your avatar in the top bar (or by clicking the "Network Profile" link on your user page on any SE site) and copying the number from the URL. For example, my network profile URL is https://stackexchange.com/users/178805/ilmari-karonen, where "178805" is my network account ID. Entering that into the query currently gives me a list of 3,625 posts, totaling about 16 MB in CSV format.