4-Bit processors have a datapath 4 bits wide. It's not a lot to work with but it is enough to get the hang of CPU architecture without getting too complicated.
Jaromir Sukuba created a 4-bit TTL CPU for the Open 7400 Logic 2012 Competition at the Dangerous Prototypes website. It's a pretty cool and simple to understand processor that he's created and documented. I don't know how he did in the compertition but it's well worth having a look at.
The APOLLO181 is a very well executed 4-bit TTL CPU. I haven't read the whole website but it looks like the author has put a lot of thought into I/O and it runs at an astounding 2.5MHz.
Updated with link to Jack's new website Here's another really good writeup scratch built CPU website. Jack Eisenmann has built a few CPU's from scratch and he describes his methodology quite clearly and has lots of Youtube videos to help illustrate his work. Great stuff!
This is a very informative writeup and description of a scratch built CPU. I have reviewed this website a few times and the information and techniques he's used to design his CPU are quite easy to grasp.