View recent responses to your posts. The little envelope next to your name at the top of the page lights up when people have posted new answers to your questions or have commented on your posts. Click the envelope to see the most recent responses to your posts and the most recent places you've gained/lost reputation.

Accepting answers. In addition to voting posts up and down, you can accept answers to your own questions. To do this, just click the check mark that appears to the left of the answer you'd like to accept (this check mark will only appear if you asked the original question). This gives the person who answered your question 15 reputation points and gives you 2 reputation points. You can "unaccept" the answer by clicking the check mark again.

Interesting/Ignored Tags. Add a tag to your "Interested Tags" list (on the home page or in the "prefs" tab in your user page) to visually highlight questions that use that tag. Add a tag to your "Ignored Tags" list to grey out questions with that tag.

Edit histories. You can tell that a post has been edited because it says something like "edited 8 hours ago" or "edited yesterday" at the bottom. If you click on "8 hours ago" (resp. "yesterday"), you can see the full edit history of the post.

View Markdown source. Suppose you're really curious how somebody typeset something in a question or answer (I think I'm not the only one this happens to). If the post has been edited, you can view the edit history (see Tip 4) and click the "view source" link above a revision. This will show you exactly what the person typed in order to get the result you see. If the post has not been edited, then it's a little trickier to view the edit history. First you have to find the number of the post. If the post is a question, then it has a url like http://mathoverflow.net/questions/number/blah-foo-bar. If the post is an answer, you can click the "link" link at the bottom of the answer to get a url like http://mathoverflow.net/questions/123/blah-foo-bar/number#number (the two numbers will be the same). Once you know the number of the post, you can get to the edit history by going to the URL http://mathoverflow.net/revisions/number/list .

Bookmark/Favorite a question. Suppose you really like a question or you really want to be able to find it easily later. You can add it to your favorite questions list by clicking the little star next to the question. Click the star again to "unfavorite" it. To see a list of your favorite questions, go to the "favorites" tab on your user page.

Use reserved characters in URLs. Sometimes your links will behave strangely in comments because they contain a reserved character. For example, the text
http://en.wikipedia.org/wiki/Castelnuovo–Mumford_regularity
ends up linking to
http://en.wikipedia.org/wiki/Castelnuovo
To fix this, you have to percent encode the troublesome character. In this case, you'd type
http://en.wikipedia.org/wiki/Castelnuovo%2DMumford_regularity
to get a good link. Here's a table (taken from Wikipedia) of reserved characters. I'll add/remove columns as I discover which characters do/don't cause trouble.

Follow up on your recent comments. It's easy to follow up when somebody replies to one of your posts (see tip #1), but you might find yourself saying, "I left a comment that I really meant to check up on later, but I can't remember where I left it." In that case, try clicking the "recent" tab on your user page. It will show you a list of all the comments you left in reverse chronological order, along with links to the posts on which you left them. It also shows you when you asked, answered, edited, or accepted an answer.

RSS feeds. MathOverflow has feeds for recent questions, questions within a given tag, activity on a single question, activity of a given user, and probably some others I don't know about. To find the link for the feed, just scroll down to the bottom of the page and click the (e.g. to get the feed for a given user's activity, scroll to the bottom of that users profile page; to get the feed for recent questions, scroll down to the bottom of the home page).

What do the colors mean? The color of the "number of answers" box and the background color of an answer tells you the following things:

Escape Markdown special characters. Characters like * and _ have special meaning in Markdown (the markup language used by the WMD editor). You can escape them with a backslash. For example, write \*test\* to get "*test*" rather than "test". You can also escape these characters in comments.

Use boolean operators on tags. You probably already noticed that you can see all questions with a given tag by clicking on the tag, and maybe even that you can combine tags to see questions that use both (by clicking on the "related tags"), but you can also search for questions that use one tag OR another or search for questions that use one tag, but NOT another. For example, the URL
http://mathoverflow.net/tagged/homological-algebra or representation-theory -algebraic-geometry
will show you a list of questions that are tagged ([homological-algebra] OR ([representation-theory] but NOT [algebraic-geometry])). NOT (denoted by by prefixing a "-") binds tighter than AND (denoted by a space) binds tighter than OR (denoted by the word "or"). See this blog.SO post for more.

Wildcards in tags. You can use ~ as a wildcard when searching tags. For example, to find all questions that have a tag ending in "geometry", go to
http://mathoverflow.net/tagged/~geometry

Restrict to certain tags in searches. When you use the search box, anything between brackets is interpreted as a tag, so the search "[ac.commutative-algebra] decomposition" searches within the [ac.commutative-algebra] tag for questions containing the word "decomposition".

See original math input. Sometimes you want to see the original input corresponding to some MathJax output. You can see it by right clicking on the MathJax output.

Search MathOverflow like a ninja. Let's face it: MathOverflow's search functionality is sometimes not so hot, but you can take advantage of the fact that MathOverflow is heavily indexed by Google. If you want to search comments or search for a phrase, you can use a google search like site:http://mathoverflow.net "wicked smooth" or site:http://mathoverflow.net "can't argue with that".

This trick can also be used to search user pages. For example, if you want to find MathOverflow users whose profile contains the phrase "finite groups", try site:mathoverflow.net/users/ "finite groups". See Google's advanced search tips for more.