There are many more up there these days and I can probably see a dozen, if not more, without trying on an average star gazing session, especially in the period just after sunset or before sunrise. I am also almost certain to have one or two moving through the eyepiece view I have looking through my telescope every night. Having said that, all these satellites don't really bother me and sometimes I just sit back and watch them for a while as they all silently pass above me. I do enjoy seeing the long ISS passes and, occasionally, I'll see a Sky - Train low over the southern horizon.
In contrast, when I first started out star gazing, way back in 1978, there were very few satellites about. In fact, they were so few that every time that I saw one I'd log the event in my early logbook! As for seeing one passing through an eyepiece view in the late 70s / early 80s, I only ever logged a single incident of that happening to me at that time (in 1981).
I used to look out for the flashes from Iridium satellites, but I believe that these are no longer up there. In the 1980s and 90s I'd also watch out for the Space Shuttle and the MIR going past. But yeah, definitely more of 'em up there these days than twenty years ago.