Thanks for the reply. I'll try to answer all the questions.
1) I'm not sure which tool I'm using. I access it through Geoprocessing -> Buffer.
2) I've tried this with many different settings. For example, 3 decimal degrees, 50 km, 100 m, etc.
3) Trying to use the check geometry tool also crashes the program instantaneously.
4) I've tried this with many files and projections. For example, a custom Albers Equal Area projection, NAD 27, etc.
5) I've tried many things. The extents range from a few 100 meters at a very local scale to continental wide lines.
Specifically, I've attached a sample project file (NAD 83) and shapefile of a simple line that I drew. It crashes each time I try creating a buffer of say 100 km. The Side Type = FULL, End Type = ROUND, Dissolve Type = NONE.