Assume the best about those making the request
The first step in my opinion is to assume the person making the request is doing so with good intentions. Different people have different levels of willingness to move. For example I am generally happy to swap seats if it helps someone out, but also have no inhibition against asking someone for a swap if it means I can be closer to a friend of family member (sometimes booking seats together just doesn't quite work out for one reason or another). This puts the interaction on a positive footing.
Respond appropriately depending on their situation
The second step is to listen to their reason for wanting to move (usually this will be given when someone makes such a request). If they say something minor like "I like an aisle seat", you can dismiss their question fairly lightly: "I like an aisle seat too, unfortunately, that's why I booked this one", they are unlikely to be much offended, because they know the request was cheeky. However if their request is reasonable (i.e. they have reason to believe that a swap would be more beneficial to them than inconvenient to you), then I would take a more polite, understanding approach.
Answer politely and succinctly, give reasons, but don't belabor them
I would say "Sorry, but I specifically booked this seat because { characteristics which made you pick that seat}". I would not use the approach of pretending to think the request was an offer (as suggested in other answers), unless the asker phrased it as such, because to me it sounds obviously disingenuous. I think that you having specifically chosen that seat is a strong argument, which many will simply accept. Tone is important — the aim is to sound firm, but not irritated by the request.
Make it clear that you are not up for argument
The asker may try to argue, or come up with an alternative solution. Avoid continuing the argument unless you are willing to be persuaded/come to a compromise. Instead simply express your unwillingness to move e.g. "Sorry, but I just didn't like moving from my chosen seat once I am settled".
Their response is their own problem
Some people will be bad tempered about having their request declined, however polite, however reasonable you are, and however good your reasons for declining. Don't take it personally, just feel slightly sorry for them ( their attitude is only hurting themselves) as you pick up your book, put on your headphones or do whatever it is you like to do to get ready for a long journey.