There are quiet a few techniques to track you. They are not limited to Browser Games.
- IP (123.456.789.123)
- Cookies (SID=uf972b3f9uvodv4et)
- Host (p12345ABC.dip.t-dialin.net)
- Browser ID (sfh924ng98erhboe8pnr389hg3p4hg34hgreladger) (I do not mean BrowserID, now known as Persona)
- Ads and (other) iFrames or data collectors (like Google Analytics, FaceBook Like,...)
- Browser Plugins (e.g. Search Bars)
Normally you can avoid this all by
- Using Brain.exe
- Using adblockers
- Disabling JS and Flash and Java and Cookies and everything else...
- Using different frequently used Proxies
- Standardizing your Browser by installing a certain package combination that is most often used
you could also just stay offline.