Compressing my collection of anime I have a lot of anime videos which are all encoded, I think, with H.264.

My question is rather simple: How can I make my 1tb collection smaller?

I know about FFMPEG. However, I do not know how to use it most efficiently. I am looking to reduce the size of the files while not causing losses in quality.

I have an i7-2700k at 4.4ghz and a GTX 770. Can I leverage my GPU's power to make this process faster and more efficient? What would be the most efficient way of doing this and what would it look like in command line form?
Re-encoding will introduce generation loss and encoder specific artefacts. Of course you are not going to encode a file 100 times and you are trying to preserve as much quality as possible, but with such vage ctriteria as encoding 1 TB of unkown quality, noise, bitrate, picture size, framerate and so forth there is much that can go wrong. Best advice: don't re-encode at all, particularly if you are not encoding from sources e.g. disks but web formats or already re-encoded content. Save the money spent on energy to buy more hard drives and learn to manage them (hint: ZFS). If you cant wait for encoder improvements and the next generation of super high efficient video encoders, then H.265 one of the better solutions currently available, but you'd have to take a close look at each file and how it was encoded, if you find that a video was already encoded on an i7 equal or better than yours with H.264 and that already took a day or more than you know you are going to spen 2 to 4 times as much. And you'd still have a bit of generation loss even if you got everything right. Also don't expect that software always returns perfect results, you should check every re-encoded file to be sure. And you shouldn't overclock your hardware or swap version numbers of software components used.

Buy a bigger drive if you don't want to go down this route, you save valuable lifetime and electricity.