Of course, no one can speak for each of the people who believes in this curse. However, my opinion is that people believe in the curse (if any really do) because it makes a good story and because many people do not think logically.
The curse makes a good story because we like to think that ancient people could do supernatural things. It sounds exciting and so we like to believe it. People then let this take over their brains. They see that some number of people connected with the mummy died in "suspicious" circumstances and they just assume it is because of a curse instead of looking, for example, at the percentage of people in general from back then who died inexplicably.
So I think it is a mix of the fact that it's a good story and the fact that people don't often like to think very hard.
The link that I have included below gives a couple of interesting anecdotes and a theory about bacteria on the tomb wall... you might want to look at it. Also, the skeptoid.com link gives a really good list of reasons not to believe.