Age does matter.
Search Engines judge sites based on lots of different factors. Some of them take age into consideration, some don't, others may do so in the future.
Some of the factors search Engines base their decisions on can be manipulated (eg: peopel can buy more links than they would normally get). Search Engines are aware of. The fact that the age of a domain cannot be faked or manipulated makes it extra valuable.
Why is age important:
Lots of domain renewals shows commitment. it shows that your site is not a fly by night get rich scam. **
Indirectly, domains with an old reg date, generally also have older backlinks. In this case the age of the domain itself does not affect your ranking, but the fact that someone was willing to link to your site for over (let's say) 10 years does. of course, if your domain was only registered 2 days ago, the chances that someone has been linking to your previously unregistered domains for over 10 years are slim to say the least.
So, yes, age matters, both directly and indirectly. Is it everything? No, it just one more factor to take into consideration.
** for that reason it's also a good idea to get links from older domains to your new sites.