This topic is about speculative biology, so if you're a cryptozoologist, well, no cookies for ya. Okay, maybe, but not for creationists who uselessly attempt to use supposed living pterosaurs as evidence against evolution. JTFFDP (Já Te Fodi, Filho/a Da Puta [portuguese sentence, so usefull for insulting])
As you can possibly imagine, speculating about a world were the K-T event didn't occured brings pterosaurs into the conversation.
The situation of these flying sauropsids in the Cretaceous is somewhat controversial; it is pretty obvious they achieved their golden age in the Early Cretaceous, when pterodactyloids produced a gigantic variety of forms, following the demise of basal pterosaurs, though anurognathids are present in laggerstaten fossil sites which only date in the Mesozoic from the Late Jurassic and Early Cretaceous (see below); interestingly, most ctenochasmatoid pterodactyloids also were found in laggerstaten fossil sites (again, see below). Pratically all pterodactyloid clades (aside from azhdarchids and pteranodontians) date from this era, and diversification within such clades is quite evident, specially in ctenochasmatoids, ranging from the very specialized filter feeder Pterodaustro to the equally specialized fisher Cearadactylus. Other clades show less extreme variations, but still notable (note the difference from the fishing ornithocheirids and the scavenging istiodactylids, both within Ornithocheiroidea).
Then, the fossil record seems to suggest a sudden disappearence of clades, and so only lonchodectids, ornithocheirids, pteranodontids and azhdarchids make it into the Late Cretaceous, and out of these only two clades survived beyond the Turonian (however, I pretty much assume the two last clades outcompeted the first two, since pteranodonts and azhdarchs only became notable in the late Cretaceous, following the dcline of the previous two clades). This, obviously, could be seen as that pterosaurs were suddenly declining and in the way of meeting a dire fate...
However, this might not be the case. As pointed out before, anurognathids are only known from laggerstaten fossil sites, and they appear in the Early Cretaceous, not just on the Late Jurassic. As a whole, these clade might actually have had a history as a Lazarus taxon, because all evidence points for a Triassic origin (they were the most basal known pterosaurs), and yet we lack Triassic fossils (and Triassic laggerstaten). Thus, its possible that they endured until the K-T event. Also, note that ctenochasmatoids were also mainly found in laggerstaten, thus probably also implying that they endured until the end.
Thus that leaves us with what? Four clades? Enough for me. Out of these clades, I'm assuming most would survive into the Cenozoic, had the asteroid not collided and ruined all the fun, except perhaps pteranodontians, because they were very specialized to a pelagic lifestyle, and the Paelocene/Eocene Thermal Maximum would probably exterminate them, as oceans are specially sensitive to climatic changes so extreme as those. Even if they survive they wouldn't pass the Eocene/Oligocene extinction event anyway. Of course, they could become smaller via neoteny, thus being reduced to small, adaptable forms. Whatever.
The other pterosaurs, well more adaptable, would obviously survive and diversify. In particular I can see a pterosaur diversity radiation lasting from the Eocene to the Miocene. Then, with the cooling of the climate, I'm assuming the flying reptiles would be hitten. Probably death to european and perhaps north american denizens, and the survivors could colonise those lands from the south, once the climate became warmer (such cycles, between retreat and return, would occur many times, since there were at least 32 ice ages in the last 2 million years).
Flightlessness in pterosaurs is likely, specially in azhdarchids and/or ctenochasmatoids, but I'd expect it to evolve only one or two times; bats never produced flightless forms after all, and while I hate the bat/pterosaur comparation I do have to agree that both were similar in one thing: the wing membrane, which extended unto the legs, would make it more difficult for them to produce fully flightless forms (birds, on the other hand, only need to loose the wing feathers to be flightless; they have their legs seperated from the wings after all). However, because pterodactyloids had reduced uropatagia, and an upright leg stance (like mammals and dinosaurs), it makes a flightless pterosaur more plausible than a flightless bat. For more info on wingless pterosaurs, see Darren Naish's post: