Is there some client like Bitcoin core, but which highly compresses the blockchain? I have been using Bitcoin Core for some months. I need a fully fledged client as I want to help the Bitcoin network. But the blockchain is so huge. I'd love to see some other client, which highly compresses it.
The Bitcoin blockchain is mostly comprised of signatures (mostly non-compressible) and hashes (non-compressible), there's some space to be gained by eliminating redundancies due to people re-using addresses but it doesn't seem to be worth the implementation cost. Using gzip -9 and zpaq -method 5 on the block files for example saves only about 20% of the total size, using a compression system with knowledge of the Bitcoin block format would do a slightly better job, but that's the sort of ballpark you would expect to see.

128M  blk00318.dat
101M  blk00318.dat.gz (30 seconds)
95M   blk00318.dat.zpaq (5 minutes)


Even a 25% or 30% reduction in the size of the chain wouldn't allow for many more people to be able to run full storage nodes, the current growth rate (2GB per month for 400KB average blocks) would make it uneconomical again in a couple of months. 

If you want to run a fully validating node to have a secure wallet or view of basic block chain data in small space, Bitcoin Core 0.11.0 does have a prune mode which can run with as little as 1.5GB of consumption- but it won't be contributing to the network at when this option is set, and your wallet use will be slightly more constrained than normal. Beyond that there's little in the way of other full storage nodes with more compact disk footprints, at least for now, pruned nodes should be made significantly more useful to the network in the future.