I do hope this is a serious question rather than just a (admittedly amusing :-) comment on the Euro crisis, because it's a good question.
Bulletproof vests generally work by dissipating the energy of the bullet. In the case of Kevlar, snapping the Kevlar fibres in the vset takes a lot of energy and this slows the bullet down enough to stop it penetrating the vest.
Any fibres with similar properties would work. Paper is mainly made of cellulose and indeed cellulose fibres have been tested for bullet proof vests. See for example http://discovermagazine.com/2009/jan/083/. Note however that the title of the article is a bit misleading as it isn't really made from paper. It's made from the same material (cellulose) that paper is made from.