I’m looking to find a movie clip of the end scene of Encino Man so I can watch Sean Astin shake his booty several times on my computer.
A) Is this a legal thing to own, IE is this copyright infringement if it stays on my computer and is only a fraction of the movie?
B) Where could I find this clip if it is, in fact, legal?
I’ve got no idea what Encino Man or Sean Astin is ore are, but I’ll give you my opinion on your legal question. A movie is a copyrighted work; a clip from the movie is covered by the same copyright. You therefore need permission to have copy of the clip on you computer. That said, the permission might be construed out of the way in which you obtained the clip: if the company offers it free for downloading on its website, I guess this can be construed as an implied consent to the downloading and storing of the clip for individual use. Still, this might be for a limited time only.
In practice there is hardly a company that offers a clip for downloading: mostly they offer streaming media that do not imply consent to storage of the clip.
The fact that you may find clips on the Internet (put there by fans) and that companies hardly ever prosecute individuals for copyright infringement by having downloaded clips on their home computer doesn’t change the above.
Ownership of any part of any movie starring Pauly Shore should be illegal. 
TTT’s exactly right. It is infringement under the law (I doubt watching booty-shaking would qualify as “fair use”). If you’ve just got the clip on your PC and aren’t marketing it, you are unlikely to be prosecuted – it just isn’t worth the cost of litigation to the copyright holder – but you could be if they so desired.
I believe you are able to use a small portion of any work without being liable under copyright law, if you are not using it for commercial benefit. Most copyright laws specify “commercial use” as the key point in prosecuting for infringement.
For instance, you could not use the clip to advertise the grand opening of your business or publish it on the cover of your magazine, but, you could probably post a few second snippet on your personal website with the caption “This is my favorite scene from the movie” without running too far afoul of any laws. They certainly won’t come after you for having it on your personal computer for your private enjoyment.
Cafepress.com has a nice help section explaining some copyright and parody laws in layman’s language.
Cillasi, you seem to think about fair use or quotations. That is not the same as keeping a clip on your computer for your own private enjoyment. In the former case you incorporate the clip because you have a further ‘goal’ in mind, for example a review or a news item. For those entirely proper purposes the law (as I understand U.S. copyright law) allows you to use snippets of the original work. The copyright owner should not be allowed to hinder the public discourse on his work.
On the other hand, the copyright owner is entitled to be paid for people that want to have a copy just to enjoy it, since that is precisely why the work was produced in the first place. That you may be only interested in a small portion of the work, doesn’t change that fact. If this wouldn’t be the case, every individual would be allowed to freely copy music CD’s as long as they were only keeping it for their own enjoyment. I’m sure that is not the way copyright laws work anywhere in the world.
All the states that have signed the BC and/or have accepted TRIPS are bound to these provisions.
True, but the fact that you will probably not be caught doesn’t change your legal position, which was what the OP wanted to know. I’m sure you mean well, Cillasi, just trying to set facts straight.