Is this a new install (or upgrade) or have you been using ArcMap on this computer for some time?
A quick trouble-shoot would be to rename the Normal.mxt so it gets re-created, but you'll need to be a local admin on the machine to perform this task.
In my experience, drawing errors are due to interruptions of some kind, due sometimes to user actions such as panning too quickly, but usually due to database system time outs and other performance problems or to references in the map to fields that no longer exist. So, I would start with a reboot and a new empty map to see if you have data access issues. Also try another machine if one is available (that would have a different map template). If you are constantly getting this error with all your data, there might be something wrong with your system configuration or your ArcMap install.