Are there any rules concerning what I can put in my profile?
Generally speaking, your profile is (to an extent) fair game, as it is a reflection of you as a person, not the site as a whole.
There are reasonable limitations for all of those, but generally speaking, unless you're a hard-core spammer or you put something truly offensive / crazy in there (like hate speech or pornography), you'll be OK.
Also, understand that all links are no-followed, so SO doesn't actually give you Google Juice from your profile.
Your profile page is yours. You can put pretty much anything on there. But I wouldn't put the following:
- Anything offensive - if you don't want your grandmother reading it, it probably shouldn't be on there
- Advertising that could be linked to spam - The fact that you sell viagra is irrelevant on Stack Overflow, but if you provide IT consulting? That could be useful.
- Profanity - Generally considered 'bad form', but I don't know if anyone has had any thing other than hardcore profanity removed.
- Offensive Gravatar images - Some people think it's funny to see Jesus on Stack Overflow. Others do not.
- A Wall of Text - No one reads those. This isn't against the 'rules'; just not a smart move.
Jeff covered some basics in this Meta answer.
Update: No, Profanity isn't removed. And there are always exceptions to the rule.
If you have to ask, the answer is "No".