Sparkym3, one of the XDA developer team member has released SparkyRoot tool for all Transformer Prime firmwares, which provides very simple method of rooting just by installing apk with a single click button.
This root app has been confirmed working on current OTAs for the ASUS Transformer (TF101) and Transformer Prime (TF201) Devices.
This includes v22.214.171.124 for the TF201 and v126.96.36.199 for the TF101.
A recent user reported that v188.8.131.52 on TF101 may have fixed this exploit but I have no further confirmation on this.
This method (as it is currently implemented) no longer works with the v184.108.40.206 ROM on TF201.
Root Transformer Prime ICS 4.0.3
Download and install SparkyRoot
Click step 1, Exploit (will move the files around and replace the busybox file)
Click step 2, Open up the ASUS App Backup tool and backup your apps
Return to this app and Click step 3 Install SuperUser to install SuperUser app
Click step 4, Cleanup, will cleanup all of the temporary files
Enjoy, your Transformer or Transformer Prime will get rooted.