I'm currently a system admin guy. I started as a certified technician with an Inter-Tel Platinum Business Partner, then went to work as the in-house admin for the company's largest customer. The jobs are very different.
Right now, I have 49 networked sites and a handful of non-networked sites. By year's end, I'll have maybe a dozen new sites, and most of the stand-alone sites will be upgraded. While my operation is somewhat larger, I'll offer some suggestions.
First, document the crap out of everything. I posted some forms that I use in another thread here. The model of every endpoint, the cable number it's connected to, every CO line and circuit number, flow charts documenting all call routing, the model and serial number of all hardware. Back this up with photos.
Putting this documentation together is a project, but will save an incredible amount of time when problems occur. Walking an off-site end-user through rebooting a piece of hardware while you're reading your notes and looking at the photo is the payoff. I once had someone ask if I had a webcam in the closet because my directions were so good!
Perform frequent backups, or schedule automatic ones. All my systems have scheduled DB and voice backups done weekly. Any major programming changes warrant an immediate manual backup. Have a system crash once without a good backup and you will become a true believer.
Second, learn as much as you can about how everything works. When a VP throws some off-the-wall idea at you, you should be able to form an intelligent assessment if it will work. After all, that's your job.
Third, have one or two people at each site be a "super user". Make them responsible for reporting troubles, requesting changes and training new users. There is no way I could allow hundreds of employees to call me directly.
Finally, maintain a relationship with your vendor. They should be your partner in keeping your company's systems up to date. Meet with them often enough so they can keep you informed of feature enhancements. I maintain hardware service contracts for all my sites, but that's a personal choice.
Remember, your vendor is in business to make a buck and they need to pay their employees as well. Buy your phones and parts from them, as opposed to shopping on-line. Saving a few bucks may come back to bite you when something goes belly-up on a weekend or holiday and you're looking for service.