|MadSci Network: Virology|
In short - yes, viral particles can and do survive outside the host (otherwise propagation would be very limited) but their 'shelf-life' varies very significantly depending on the kind of virus and on the environmental conditions.
The details of ex-host survival vary greatly. Some viruses can persist for months on surfaces and in aerosols while others only last a few minutes. Some viruses can hitch a ride on insects, fungi, or worms - even to the point that virions get 'packaged' together with the fungal spores for long-term storage and transmission. Viruses of bacteria and protists can survive in water and may be transferred from resevoir to reservoir by wind-borne droplets.
So, in conclusion - yes, we encounter billions of viral particles daily (and viroids as well) and it's a good thing that most of these are not infectious for people. In fact it seems that the majority of viruses responsible for human disease are actually not very stable outside the host and die off rapidly. There are notable exceptions such as poxviruses and others.
Try the links in the MadSci Library for more information on Virology.