After Googling a bit about the TI Stellaris Launchpad, I found out that it can be used as a 10Mhz 8 Channel Logic analyzer with some small free softwares. The plugin's home page can be found here and please refer it for the further information about the functions.
You have to download following for this,
First of all you have to unpack the both files for two folders. Then copy "ols.profile-SLLogicLogger.cfg" file from the plugin to "ols-0.9.6.1\plugins" folder.
Then we have to flash the code into the launch pad. You can flash "sllogiclogger.bin" in the plugin to the launchpad using TI LM Flasher. If you are a linux user, you can refer to my previous post on flashing Stellaris Launchpad on linux.
Now you can run "ols-0.9.6.1\run.bat" to run the logic analyzer. If you are using Linux, you can run it using "ols-0.9.6.1\run.sh" .
In Logic Sniffer, got to Capture->Begin capture and set the configuration as below. Please note that you have to select COM port (here COM47) according to your Stellaris Virtual port on device manager.
Here I'm testing 3.3V Logic '1' on PB0 pin of the launchpad which is the Channel 0 in the logic analyzer. The results was as on the picture and it was a success. So now you can have your own logic analyzer with TI Stellaris Launchpad.