although League of legends is another DOTA game made by the creator of DOTA my brother who was a DOTA addict is now a LOL addict google league of legends its free and its a VERY good game it blows dota out of the water
Use Titanium Backup (free from the market) to back them all up.
Otherwise use a file explorer such as Estrongs and then menu > Manager > App Manager, hold any one app > Select All, menu > Backup. The APKs will be backed up to /sdcard/backups/apps.
If you're more technical I could detail a method to pull all the APKs via adb.