What are the pros and cons of choosing my own research topic? (This question is one of three correlated questions: Can I get enough help? (first part), How should I do it? (second part).This is the third part.)

I am an undergraduate student (in Computer Science and Engineering) and I will be starting undergraduate research for my thesis. I have talked with many professors about possible projects and all the projects they proposed to me seemed interesting enough. 

During summer, though, I read a paper and I was very interested and excited about it, but this paper was not for the projects that were proposed to me, but in a different area. I would like to do research in this area but I have some questions, because none of my professor is doing research in this particular field.

So, my questions are:


What are the downsides of choosing my own project instead of
doing a project that a professor is working right now (with his
Ph.D. students)?
How harder will it be to get something good out of it (in
comparison with doing a proposed project)?


P.S. I want to understand whether it will be beneficial to do a project that I want to do because of some paper(s) that I read or it will be better to do a project that was proposed to me. Also, I would like to go for a Ph.D. after I graduate.
Along the lines of earthling's answer, you do have a strong say in your topic, and you'll definitely want to be interested in the topic as you'll be putting a lot of work into it.

However, do realize that, as an undergraduate, you have far less experience in doing research than your advisor. You will save yourself a tremendous amount of work and effort by working closely with him on your project. One way to ensure that your advisor will be willing to invest that time in you is to work on a project that (1) interests him and (2) is related to his research. Even better, both. You are definitely free to choose whatever project you want, but it would be a good idea to choose something on which he can offer his expertise.