Is there software that can view .dwg files?

DraftSight. It doesn't cost money and they'll give you a nice .deb installer... but it's not open source or free software.

On the upside, it will also let you create and edit .dwg files.

LX Viewer (source: http://sourceforge.net/projects/lx-viewer/files/ )

LX-Viewer is a program that will allow you to open, view, print and convert DWG or DXF files, typically used in AutoCAD related technical drafting. The most important feature is that LX-Viewer allows you to manipulate your DWG data on the Linux platform. You may zoom and pan the drawing as you would in AutoCAD. Files can be saved to DWG or DXF formats from AutoCAD version 2.5 to 2002, also as BMP, SVG and PNG formats. Files can be printed or plotted to a Postscript printer or to file. Multiple files can be batch converted or batch plotted. Layer states can be changed (on/off, freeze/thaw, etc) with a full layer dialog. The paperspace/model space toggle is fully implemented, as is the ability to select among various paperspace layouts for AutoCAD drawings.

I use ODA Drawings Explorer (formerly known as Teigha Viewer) available from the Open Design Alliance, and also the ODA File Converter (formerly known as Teigha File Converter) from the same provider. Packages are available for Ubuntu. It is freeware but not free nor open source software.

ODA Drawings Explorer incorporates the power and flexibility of ODA into a single application that can render both .dwg files and .dgn files using a common command interface for both formats.