A while back, I posted about my desire to see GeoJSON supported as an output format from ArcGIS Server. I found myself needing that capability so I recently completed, and posted to GitHub, a first cut at a server object extension (SOE) for ArcGIS Server 10.1 that enables output of GeoJSON via an HTTP GET.
Using the SOE is fairly straightforward. If you download the code and build it (ensuring you have installed the ArcObjects SDK for .Net), you can simply move the project outputs to your target machine and use the ArcGIS Server manager to install the SOE. Once you log into the manager application, click “Site” at the top of the page and then “Extensions” on the left. Click “Add Extension” and browse to the .soe file. You should end up seeing something like this: