I suspect that this will become a bit of an essay, but hopefully it may be of interest to others. I have no concrete figures on numbers caving, here or abroad, but I may be able to pass on a little of what I have noticed in the past 20 years or so.
Are there less people caving in general in the UK? I am pretty sure this is the case, a good example is how crowded places like Priddy Green used to be compared to now. Is it a dramatic drop? I am not sure that it is, and I am also sure that Andy F is right when he says that there is now a much wider selection of activities for people to choose from is partly the reason for this. Also in an image obsessed society caving is hardly the the sexiest of outdoor sports (no chance to strut your funky stuff in front of amazed mere mortals due to the rock above you somewhat spoiling the view).
I also agree with mrdoc that the number of diehards is not decreasing much, i.e. we are getting fewer cavers in, but people seem to be staying on the scene longer. I am not sure I totally agree with Scutchamer or Vance. My own club's membership has been almost exactly constant for about the last 15 years. Uni clubs becoming more popular? I think using CHECC as a measure is not a particularly brilliant measure, as it has not been going all that long (six or seven years?). Also individual uni clubs do wax an wane. My uni club went from 12 members in 1994 (and almost dissolution) to 30 odd in 95 and about 60 odd in 96, so this sort of growth has happened in the past, this growth was almost entirely due to a new injection of members in 95 which raised enthusiasm. Interestingly these people were mature students who were members of established clubs! I also totally disagree with Rich, established clubs are very good at recruiting uni cavers. I would say that my club's membership is about 85% made up of ex-uni cavers, many of whom decided to join after staying at our hut. This is an effect that continues to this day, several joining at our last committee meeting (April).
As to abroad? Well I think that Peter is a little harsh saying that UK cavers are too introverted to care about what happens beyond our own shores. Just look at any copy of Descent at the amount of foreign expeditions going on, many of which are actively promoting caving as a sport/science in country. As to decline? I am sure this varies from country to country but based ona reasonable experience of countries (Europe, Americas and Asia) I seem to get the impression that in all of the countries I have visited interest in caves is increasing.
Finally I think that the comments by Pitlamp and Andy Morgan are very important. Club membership is not about taking advantage of club facilities. The club is far more than the sum of its parts, and as an individual I would say that you get out as much as you put in. It does seem fashionable to deride the established clubs on the web, however I for one think that UK (and probably world) caving would be all the poorer if they were replaced by "groups of individuals".
Ed