Syslog-Server
A complete syslog server! You can turn on the network logging feature on your network devices such as a WiFi access point or an Ethernet router, run this syslog server on your android device and collect logs from them. For more information about syslog visit http://en.wikipedia.org/wiki/Syslog
Main features of SysLogServer:
Collects logs from many devices.
Starts on boot.
Keeps WiFi awake.
Writes log messages to SD card.
Shares content of the log window.
Note, that this server does not require ROOT permissions and can use ports greater than 1023. You can use 514 on a rooted device only.