We manage hundreds of domain names for clients and have a few different processes.
First, we renew for multiple years whenever possible. This reduces the need to renew year after year, and we can usually take advantage of multi-year renewal discounts. For these we then put an entry into the system administration schedule to review the WHOIS information every year, and then an entry to renew again 90 days before it will expire.
Next, we use automatic renewal with the registrar for some names that renew every year. This helps to ensure that they get renewed even if we don't get the notice for whatever reason.
And finally, we have an e-mail address setup specifically to receive domain renewal notifications. This goes to a few different people here at the office. I am responsible for receiving those and processing the ones that need to be handled. If a notice comes in for one that is less than 30 days out, then a couple of other people in the office know to either come bug me about it or check with the client and handle it if I am not available (vacation or whatever).
I wrote up a blog article a while back called The Importance of Domains that outlines some general tips for domain name management. It's aimed at clients, but anyone who owns a domain name may benefit from it.