Are there any special requirements for how I format the text in my hyperlinks in my web pages?

Basically, you should make sure that your hyperlinks contain text that is descriptive of the page you are linking to. This seems obvious, but if you're not thinking about it, you may do something like the following: Click here to play Diamond Slide. When you have a link like the one above, you are really saying that your page is about "click here". When in fact, it is about a game called "Diamond Slide". 

So a better link would be: Click here to play Diamond Slide. 

Even better would be a link like this: Click here to play the Diamond Slide Game.

Why does this matter? There are two reasons:

• It can improve your search engine rankings. Some search engines will use the text in hyperlinks to help determine the relevancy of a page. So the first example tells the search engine your page is "relevant" for the search term "click here", while the second example tells the search engine your page is "relevant" for the terms "play" and "diamond slide." Why is the third example even better? Because it informs the search engines that the link is a game.
• Website visitors with physical disabilities may have a hard time following links like the first example. The reason is that users with some handicaps may view a web page by "tabbing" through the hyperlinks, and looking at the text of the link.

2016 update: Remember that Google and other search engines are very complex algorithms for predicting the kinds of content people want to look at. They are complex, but they're still just algorithms, and they are prone to being duped by people who want to subvert the algorithm. The fact that link anchor text can affect a page's ranking led to something called "Google bombing," which is what happens when a large number of people all put the same anchor text leading to a specific page. For example, a group of people Google bombed President George W. Bush by making links to his White House biography that had anchor text: "miserable failure." Thus, when people searched "miserable failure," they were directed to the White House page for GWB.