JailbreakMe

This was the exploit used to easily jailbreak 1.1.1 phones. Users would simply go to jailbreakme.com on their iPhone and select the bottom link.

Credit
metasploit, rezn, dinopio, drudge, kroo, pumpkin, davidc, dunham, planetbeing, NerveGas

Originally found by cmw.

Exploit
There was a buffer overflow in the iPhone's libtiff. This was exploited to run a small application to jailbreak and patch libtiff. This exploit was also used in the PSP. The source code of the exploit was later released by cmw on his blog.