It is possible to publish a .mxd in OpenLayers? I am using ArcGIS 10.0.
Short Answer: No, not directly
Long Answer You need to understand that these are two different technologies.
a ArcMap Document (.mxd) is a file which tells ArcMap which layers to use and how to render them etc.
A .mxd file can only be opened in ArcMap, but if you have ArcGIS server, you could then publish that map as a MapService, which could then be consumed in a custom OpenLayers based Application.
Yes, it is possible, if you use ArcGis Server. There are 2 steps:
1) publish your ".mxd" (really, there are data [stored in gdb, or enterprise geodatabase, or another source] and .mxd)
You could create tiles of your .mxd and then publish those to an open service such as OpenLayers.