It's not... impossible to get accepted without a degree ... but I think it's something like 98% of people accepted have at least one, or will have one by the time they start school.
Think about it, there are so many applicants, and the vast majority of them have degrees. Someone without a degree would need to really go above and beyond to prove themselves, because even though it's only one more year of work, having that degree is an accomplishment.
Now, if you're a non-traditional student, it may be a somewhat different story, but you'd be best off calling some dental schools and seeing what they say in either case.