Papercrete Walls
Papercrete is just adobe/cob that uses recycled paper in place of the straw, although unlike cob or adobe, papercrete generally uses more of the insulating material, at the expense of a lower compressive strength. It seems likely that it is not possible to build a wall with papercrete, that is both structurally strong and highly insulating (although its certainly easier if you don't have to deal with earthquakes, hurricanes and large snow loads). Although the blocks are typically quite thick, the required amount of cement will reduce the R-value significantly below that of cellulose, which is the equivalent insulation-- at least for load bearing structures.
The alternative is do to post and beam structures and use the papercrete as infill in the same way you do with strawbale or straw-clay. There is still no real lateral structure, so like strawbale you will need to rely on stucco wire, corner bracing or some other technique.
Most of the early Papercrete buildings are load bearing and built in areas where building permits are not required, but there seems to be a movement toward post & beam structures instead. There is now (2013) at least one commercial manufacturer Mason Greenstar.
Papercrete Blocks
Papercrete wall. Completed building in background
The main advantage is the use of waste paper as a building material, and the potential to achieve highly insulating walls that are fairly rot & insect proof. As a building technique this is one of the fringe movements that hasn't gotten much attention, even in the green building community.1
The disadvantage is that in order to get high insulation, you want to use a post & beam structure, and the resulting structure still won't likely withstand earthquakes. The material is also likely very vapor permeable and probably absorbs quite a bit of water. Most uses have been in very dry climates.
Summary: An interesting idea that hasn't caught on, and will be a challenge if you have to deal with a building inspector and/or are in an earthquake zone.
Notes
1: Exactly why is unclear as waste paper seems as viable as waste straw, but certainly building with straw is a much more developed technology.