If your dox have been posted: Wearelegal has a strict non-removal policy. What this means is that if your info goes up, it's not coming down unless it's bad, old, or otherwise inaccurate. Cover your tracks and you won't have to worry about it. Otherwise, you're just going to be made fun of in #wearelegaldoxed and on Twitter.
For site visitors:
The only IP retained in the access logs is 127.0.0.1.
Access logs are only kept for up to 72 hours. They're only retained this long in case something goes awry with the reports (See below).
The only "real" info I get in the logs is your user agent string.
If you came to this site via another site, the URL to the site you came from is in the referer section of the log entry.
Your browsing habits on this site are not disclosed to third parties, unless your user agent is Internet Explorer/2.7 or something equally silly
Reports of the day's overall traffic are generated daily. These reports only contain how many times each page was visited, how many times each referer was used, and how many times each user agent string was used. These reports are usually kept private, but when they're not, they look like this.
One final bullet point: If you don't brag about it, nobody will ever know that you were the one who posted it.