This is a major issue in IT; we face it all the time. I would personally recommend several things.
1. Don't take your boss by surprise.
In other words, don't just mention out of the blue, "Say, we need to upgrade our servers," or pop it on him while he happens to be walking through your section. Either write him a detailed e-mail (concise, mind you!), request a short meeting, or even write or print it up on paper. Your boss will take something more seriously if (s)he can see that you take it seriously.
2. Make comparison
This is a key point that I have found quite effective. It works best in a real interview, which I try to steer something along these lines.
I really don't see the need for this equipment. It doesn't appear to produce much if any ROI (Return on Investment).
Mr. XXX, how often do you replace your cell-phone?
Boss: (usually a bit surprised)
Well, usually I replace it every 2 years, but what does that have to do with anything? That's a personal expense, not designed to produce an ROI.
Mr. XXX, my point exactly. I do the same thing. Why? Because it's more convenient to be up to date. Because the newer equipment usually works better. Because the newer equipment should save time. Not because there is a definite or precise ROI, just because it is a useful tool.
It's the same way with our servers. We don't need new servers; the old ones are still working. However, it would improve our company, in that it is more convenient to be up to date, it usually saves time, works better, and overall simply improves company morale and spirit.
Furthermore, in your programmers' eyes, new equipment tends to make the company appear a more desirable place to work, which will give you more satisfied employees and a greater hiring capacity.
3. Link to something tangible.
As I did in the last paragraph of that interview, that link doesn't need to be financial. But whatever it is, you should be able to demonstrate to your employer how (s)he and the company will benefit from this newer equipment.