At the present time the inflationary theory, which a few years ago was in significant conflict with observation, now agrees very well with our measurements of the mass density and the non-uniformities of the cosmic background radiation. The evidence for either inflation, or something very close to it, is very, very strong.
I'd just like to close by saying that although I've been using the word "theory" in the singular to talk about inflation, I really shouldn't. It's very important to remember that inflation is really a class of theories. If inflation is right it is by no means the end of our study of the origin of the universe, but it's really still closer to the beginning. There are many different versions of inflation, and in fact the cyclic model that Paul described could be considered one version. It's a rather novel version since it puts the inflation at a completely different era of the history of the universe, but inflation is still doing many of the same things that it does in other theories. There are also many versions of inflation of the more traditional type. There's a great deal of flexibility within the inflationary picture, so there is still a lot to be learned. The continuation of this work will involve both the study of cosmology and the study of the underlying particle physics, which is essential to these models. The intersection between cosmology and particle physics us likely to remain an exciting area of science for many years to come.