Are there any practical implementation of a homomorphic hashing or signature scheme? A homomorphic hash function is a function $H : A \to B$ between two sets with some algebraic structure $(A, *)$ and $(B, \star)$ such that


$H$ is collision resistant, i.e. it is hard to find $x \neq y$ such that $H(x) = H(y)$ and
$H$ is a homomorphism, i.e. $H(x * y) = H(x) \star H(y)$.


Are there any practical realizations of such a homomorphic hash function, or even a homomorphic signature scheme (i.e., where we can "add" valid signatures to get a signature of the "sum" of two messages)?

Even better, are there even any libraries implementing this?
There's plenty of research in this area.  I'll give you just a small sampling:


Speeding Up Homomorpic Hashing Using GPUs. Kaiyong Zhao.  ICC 2009.
Transitive Signature Schemes. Silvio Micali, Ronald Rivest. CT-RSA 2002.
Homomorphic Signature Schemes. Robert Johnson, David Molnar, Dawn Song, David Wagner.  CT-RSA 2002.
Sanitizable Signatures. Giuseppe Ateniese, Daniel H. Chou, Breno de Medeiros, Gene Tsudik. ESORICS 2005.
Linearly Homomorphic Signatures over Binary Fields and New Tools for Lattice-Based Signatures.  Dan Boneh, David Freeman. PKC 2011.
Homomorphic Signatures for Polynomial Functions.  Dan Boneh, David Freeman. Eurocrypt 2011.
Homomorphic MACs: MAC-Based Integrity for Network Coding. Shweta Agrawal, Dan Boneh. ACNS 2009.
On Homomorphic Signatures for Network Coding.  A. Yun. IEEE Trans. Computers.


Like I said, this is only a small subset of the available research in this area.  I found most of these through about 5 minutes with Google Scholar.  I recommend you start by doing a literature review to familiarize yourself with the research literature on this subject: search to find as many relevant papers as possible; read each such paper; for each paper you find, read the related work section and bibliography to try to identify other relevant papers, and also use Google Scholar or other sites to find other papers that cite that paper that might be relevant; for each additional relevant paper you find, repeat the process.

After you have done this process, you should be in a better position to ask a more narrowly targeted question with a particular set of requirements -- or, if you're lucky, you might have found a solution to your particular problem already described in the literature!