I have ArcGIS Desktop 9.3.
Is Buffer only available with an ArcInfo (called Advanced from 10.0) or is there a way to buffer with an ArcView (called Basic from 10.0) level license?
ArcGIS is the software suite name, whereas ArcView, ArcEditor, & ArcInfo are licensing levels for ArcGIS.
ArcView has limited buffer options, and ArcInfo has the full, advanced buffer options (see bullet point #4 under "Usage Tips").
Buffering is allowed in all licences (ArcView, ArcEditor & ArcInfo)
Full License Matrix for 9.3 is here: