In some cases, it seems like coercion or outright theft. Boudica, a queen of the Iceni, rebelled against Rome after her husband, Prasutagus, left his kingdom to Rome and his daughters jointly to repay debts incurred earlier, or so Roman historians would write. That ended as badly as can be expected, and after Rome seized it all, flogged Boudica, and raped her daughters, the Iceni followed the warrior queen to battle. Cities, inclding London - or Londinium at the time - were burned by the Celts, but eventually the Romans defeated the more poorly trained and equipped tribesmen. So... paying off debt seems to be the surface reason, but also, I'd have to guess that Rome wrote that into history in some cases after they'd already annexed their new acquisition.

Here's the Wikipedia link for a quicker read if you want.

Ptolemy XI left his Egyptian kingdom to Rome in his will (maybe -- a will was produced as having been lodged in Rome that made this provision, and required Ptolemy XII to bribe Caesar to ignore it, although it was still used to justify the annexation of Cyprus), but Rome did not attempt to enforce this. Egypt was in something of a mess, and Ptolemy XI was installed by Sulla as a pro-Roman king; he had been required to marry Cleopatra Berenice, but mysteriously chose to murder her. Because she was more popular with the locals than he was, Ptolemy XI was promptly murdered by the people of Alexandria. This made it unlikely that his subjects would be terribly likely to accept his having submitted them to Roman rule, so Rome did not contest the inheritance of Ptolemy Auletes in Egypt and of his brother in Cyprus, at least for a little over 22 years, when they annexed the island.

(apologies -- edits because I can't spell today, let me know if I typed anything else horribly)

I did an undergrad essay on Pergamum so I can shed some light on that kingdom until someone more knowledgable comes along. From what I read it was becoming apparent that while Pergamum was not a vassal/client state of Rome, it was almost a roman dependency. Two major wars had been won with the extensive military and diplomatic support of Rome that basically gave Pergamum hegemony over Anatolia. If Roman support was withdrawn, IE pergamum started backing the wrong horse, it was not without reason that they would be on the losing side of the next war and suffer greatly, and that even should the relationship merely cool, Pergamum would still suffer for this lack of support.

At the time of his death, Attalus III did have no heir, was very aware of the relationship between Rome and his kingdom and if I recall correctly, also aware of some internal strife that had recently been settled somewhat. His decision to bequeath the kingdom to Rome could have been in tacit aknowledgement of Pergamums status increasingly becoming a Roman Dependency, or perhaps a more altruistic reason of wanting to prevent civil war in a successio crisis, which were very common in the ancient world. Of course in politics altruistic reasons should be looked at with heavy scrutiny, so it is my opinion that he it would have been a combination of both, mixed perhaps with some roman pressure/promises of intervening in Pergamum in the event of a succession crisis, as they were wont to do throughout history. Had they done this, a puppet king would have been installed who was pro roman, so it was perhaps better to be done with the pretense and spare the bloodshed.