Age of a domain is a determining factor also - the older it is, the more perceived authority that it has, however the expiration date has been playing a role in things now too.
This is something that was released by google a few years ago:
Certain signals may be used to distinguish between illegitimate and legitimate domains. For example, domains can be renewed up to a period of 10 years. Valuable (legitimate) domains are often paid for several years in advance, while doorway (illegitimate) domains rarely are used for more than a year. Therefore, the date when a domain expires in the future can be used as a factor in predicting the legitimacy of a domain and, thus, the documents associated therewith.
Google has never openly stated that they do not use this as a determining factor, however they have never denied it either. You'll find plenty of information on the web for both sides of the argument (just like everything else with SEO)