I thought the solution was to take a bunch of old transactions, hash them, and replace those transactions with the hash. Though it's a one-way process, if someone has the original transactions, it's verifiable.
This is functionally what the merkle tree does. Each transaction has it's own hash, which is then included into a binary hash tree with one other transaction, and then each of those hashes are paired and hashed again to form the full merkle tree. The last hash (merkle root) is included into the block header, which is then hashed again when the next block includes it into it's own header, thus forms the 'chain' part of the blockchain. That merkle hash root inside the block header is intended to represent that entire block (in the sequence of the lifespan of the blockchain) once every transaction included into that block has been spent. Presumedly in the future a great many blocks would be reduced to only the 80 byte, fixed length, headers after a few years time. There are already several blocks that could be pruned down this way to only those headers, but the pruning functions have not yet been implimented into any client that I am aware. Mostly because it's not consider a pressing need at the moment.