I visit my own profile at least once (usually several times) every time I get on an SE site. This is almost always SO, but I'll check my profile on every site where I've an account when I visit. I'll check in at least four times a week, usually five or six. My most common actions, in descending order of frequency:

- Check flagging results. By a *vast* margin, this is what I use my profile for most often.
- Examine details of reputation changes. 
- Look up comments which have pinged me. This is often a result of seeing only a partial comment in the notification area.
- Search for a particular question, edit, answer, or comment I've made.
- Check suggested edit results, when I have < 2000 rep. This is generally used only if one is rejected, which is a rarity. If I had more rejected suggested edits, I would check it much more frequently.

On someone else's profile:

- Examine their questions, answers, or activity history. This is usually done to check if they've posted duplicate questions, or to get a sense of their general writing style and asking/answering abilities.
- Look up contact information.