If the paper is in your field, you probably have a sense of the impact. But if it's outside of your field, it becomes trickier. A pretty good proxy is how many times the paper has been cited. Pretty much all the work in the study of language over the last 50 years has bounced off of Chomsky's ideas, and you can see this in the fact that his 1965 book Aspects of the Theory of Syntax has been cited 11,196 times...and that's only one of several very influential books.
It takes a few years for a paper or book to start getting citations, though, because it takes time for people to read it, not to mention the fact that a paper that is printed today was probably written anywhere from 1-3 years ago. So for a new paper, you can estimate how big an impact it will have by looking at the quality of the typical paper published in the journal in which the paper in question was published. This is usually measured by -- you guessed it -- how often papers in that journal are cited.
As a recent article in the Times points out, this gets tricky when you want to compare across fields. In some fields, authors meticulously cite everything that could possibly be relevant (linguistics is a good example). Other fields don't have as strong a citation tradition. Conversely, researchers in some fields traditionally work for years at a time on a project and sum up all their findings every few years in a single, high-impact publication (again, linguistics comes to mind). Other fields are more concerned with quickly disseminating every incremental advance. Then there is simply the size of the field: the more people in your field, the more people can cite you (developmental psychology journals tend to have low impact factors simply because developmental psychology is a very small world).
So by looking at citation rates, you might conclude that molecular biology is the most important field of modern thought, and mathematics and computer science are among the least. I'm a fan of molecular biology, but it's hard not to admit that molecular biology would be impossible without recent advances in mathematics and computer science; the reverse is not true.