I have yet to find a good, comprehensive reference of abstract algebra structures, so I decided to write one myself. Here, you'll find the various structures that are studied by algebraists and a brief description of what properties they require. This is NOT a reference for abstract algebra proofs or results; it is a library of definitions and relations between structures.
NOTE: This reference is under construction, so you should expect to see changes over time. If you find any errors, feel free to get in touch with me.
There are two ways to browse this reference. You can view the full list of structures if you're looking for something specific, or, if you're just perusing, you can start from Set and build up a structure of your choice.
By the way, this reference is typeset using the wonderful MathJax library, which allows you to embed TeX and several other mathematical typesetting languages directly into HTML. It's free to use and I highly recommend it if you're tackling any similar projects.