For a more ‘complete’ list of fallacies, you can easily look up online resources such as the Fallacy Files, amongst many others.
However, fallacies are simply errors in reasoning, and there are just too many ways in which this can happen. Attempting to memorise them is, at any rate, besides the point; as mentioned in class, the idea is to become more sensitive to such errors. Naming the specific fallacy is much less important than understanding the error.
(For any comments to this post, pick a fallacy that you may have noticed being used – especially by yourself – and explain why the reasoning seemed to work, but is actually not as strong as thought upon closer analysis.)