Where can I find research papers to read? (not currently in academia) I have graduated from university and am no longer enrolled. Even while there, I didn't really have any experience finding and reading research papers written by others.

Is there an online database where people post their papers so that others can download to read? 

Looking for a list of these databases/websites. Paid is okay too.

Update After reading the comments and answers below, I'd like to add that I am looking for research papers in the Computer Science / Computer Engineering / Electrical Engineering fields, and that I have graduated a few years ago from an undergraduate Computer Science program. I have not attended graduate school nor pursued a PhD.
This is going to depend a lot on your discipline. Some disciplines are very good at keeping papers and preprints publically available. For example, most math and physics papers get papers put up on the arXiv but this is rarer in other fields. Some other fields put papers up on SSRN, but some fields don't up up almost any preprints. 

It isn't clear from your question if you've completed just your undergraduate or did some graduate work. Given your statement about not having looked at papers before, I'm guessing this mean that you have either finished just an undergrad or finished a master's but nothing beyond that. If that's the case, I'm also not sure that finding papers will in general be useful for you. It might help to clarify why you want to find papers and what your goals are.