Loggy (root)

Loggy is a handy tool for developers that lets you view your logcat in your desktop browser. You can also view the contents of your SD card.

Loggy is open source:
https://github.com/koush/Loggy

FAQ:

Q: AGHHH! WHY DOESN'T LOGCAT WORK ON INTERNET EXPLORER?
A: ARRRRHHHH WHY ARE YOU USING INTERNET EXPLORER? IT DOES NOT WEBSOCKETS!!!!

Q: Hey bro, why does Loggy need root?
A: Well bra, it's because as of JellyBean, apps can only access their own logs, and not the system log or other app logs. So root is required to see the full log. https://plus.google.com/103583939320326217147/posts/2Yb5wgrx5ib