You only need the recent part of it that deals with the bitcoins you own or receiving or storing.
Right now, everyone stores the whole thing because the blockchain is still pretty small.
But as time goes on, it is likely that the average user won't hold the whole blockchain on only large servers or "bank"-like entities will keep the whole thing.
Excelent, if this is correct, lets do it!
The whole thing could be made avalible as a download by the offical site and backed up elsewhere, maybe as well as being stored in a way that makes it's size more logarithmic over time.
But clients that are designed to exist all over the place, maybe even web clients like most exchanges, they need only store what they use as they use it.