As you say, this was quite common in the Roman Empire. Indeed, many of the 'better' Princeps were adopted (the Five Good Emperors for one, and it is notable that Commodus who was the son of Marcus Aurelius was a horrible ruler -- trivia-wise, I believe Commodus' succession to be the singular mistake Marcus Aurelius made if you were to take Edward Gibbon's view on him).
Other than the Romans, the Japanese custom of adoption was used sufficiently. The Tokugawa, for one, had a number of side-branches which served the express need of the main family and allowed sons to be adopted in when necessary. The last Shogun, for example, came from a minor branch. The Wikipedia article doesn't list the full complexity which is documented nicely in his narrative biography, 'The Last Shogun' by Ryotaro Shiba (disclosure: that link is to myself but it is difficult to find good sources on Mr Shiba in English and he is well worth reading). Note that even though the Tokugawa and the Matsudaira (Yoshinobu's original family) were relatives by blood, they were not allowed to inherit. Therefore the adoptions within the family branches were necessary to allow the inheritance to come to Yoshinobu. The Tokugawa have a few other examples I believe from the 18th and 19th centuries, but they would have kept the adoptions within the general branches mentioned above.
I believe the previous Kamakura and Ashikaga shogunates used adoption less, but in general the Japanese have/had no qualms about familial adoption by the ruling classes.
Insofar as I am aware, the Hellenistic kingdoms were less keen on adoption and succession generally followed a family line. The same I believe was the case in the various Persian kingdoms.
Indian history has some interesting examples based on Wikipedia, but I don't know if that applies to their ruling classes as well.