2 Popular engines:
used in Firefox, Camino, Flock, SeaMonkey, K-Meleon, Netscape. Original development by Netscape, currently develop by Mozilla
used in Konqueror, WebKit, Safari. Develop by KDE (for using with Konqueror). It is small library, most mobile phone used it!
For another library, check out: Trident, Tasman, WebCore, Presto, iCab. Did you know? and it have not only these. Please visit wikipedia: List of layout engines page for full list!
Internet Explorer (Microsoft) used Trident, but IE for Mac they use Tasman). Presto using in Opera and WebCore is KHTML + KJS (Java Script) using in Safari.
check out for compare
You can visit blognone: Browser. They have many web browser update news. (Thai Language)
Engines list: Trident · Presto · Gecko · Tasman · WebCore · KHTML · iCab · Prince · GtkHTML · Gzilla · Boxely · Tkhtml · Robin