I've tried a couple of smaller projects that were less than successful.  The best success I've had is using cardboard furniture ideas to make something out of cardboard first -- so the piece has structural integrity based on the cardboard construction. 

I laminate 3 sheets of corrugated cardboard together using Weldbond II wood glue -- with middle sheet of cardboard corrugations perpendicular to the outside sheet.  That increases the strength of the pieces.

First I cut my pattern pieces out of cardboard and then laminate them, and then assemble them.  I weight and clamp the cardboard while it's drying to ensure it stays flat and joints stay tight. 

Then cover the whole thing with several layers of papier mache.  But the papier mache is more of a decorative element for me. 

There are several tutorials online for constructing cardboard furniture.  Creativeman on Instructables has several.  Here's one where he makes a small side table. 

http://www.instructables.com/id/Make-Fu … Cardboard/

theRIAA has one making a table from cardboard lumber as well:

http://www.instructables.com/id/Cardboard-Lumber/

If you understand french Eric Guiomar has some videos online and a dvd / books as well.  The techniques are fairly clear from the online videos even without understanding the language.

Hi,
I brought the DVD from Eric Guiomar - It didn't really show as much as I had hoped, but I was still able to work out the technique and adapt it to make all kinds of furniture out of cardboard. Have a look at the cardboard furniture photos - they are amazing!!!
http://www.compagnie-bleuzen.com/vignette1.htm