It should be noted that the following list has not been updated since November 2014.
The following browsers do support SNI:
- Internet Explorer 7 or newer, on Windows Vista or newer.
- Mozilla Firefox 2.0 or later
- Opera 8.0 or newer (TLS 1.1 protocol needs to be enabled)
- Opera Mobile with at least version 10.1 bèta on Android
- Google Chrome (Vista or newer. XP on Chrome 6 or newer)
- OS X 10.5.7 or newer on Chrome 5.0.342.1 or newer
- Safari 2.1 or later (Mac OS X 10.5.6 or newer and Windows Vista or newer)
- Konqueror/KDE 4.7 or newer
- MobileSafari in Apple iOS 4.0 or newer
- Android default browser on Honeycomb or newer
- Windows Phone 7
- MicroB on Maemo
The following browsers do not support SNI:
- Internet Explorer, all versions, Windows XP
- Safari, Windows XP
- BlackBerry Browser
- Windows Mobile 6.5 and lower
- Android 2.x default browser
The following HTTP (web) servers do support SNI:
- Apache 2.2.12 or newer with mod_ssl
- F5 Networks Local Traffic Manager with version 11.1 or newer
- LiteSpeed 4.1 or newer
- Pound 2.6 or newer
- Apache Tomcat or Java 7 or newer
- Microsoft Internet Information Server IIS 8
- PageKite tunneling reverse proxy
The following HTTP (web) servers do not support SNI:
Edit: Apparently there's a more complete list at Wikipedia :) (thanks @Tom Brossman)