This is a subject on which there are probably as many opinions as there are people. It's kinda like asking a roomful of beer drinkers to name the best beer (free is always good).
Here's my $0.02 worth:
1. A 3,000 mile oil change interval largely dates back to a point in time when technology, for both engines and lubricants, was nowhere close to the level that we enjoy today.
2. The last car that I recall seeing a no-kidding 3,000 mile oil change interval listed in an owners manual was the original VW beetle. In an air cooled engine, the oil also serves as the cooling medium, and as such it is subjected to much more punishment (heat related breakdown) than the oil in a water-cooled V-8 engine that is either unmodified or slightly modified. Anyone who has ever owned air cooled VW can tell you how critical 3,000 mile oil changes were to keeping those cars alive. Even the 86 Nissan 300ZX Turbo that I owned called for a 5,000 mile interval, with a 3,000 mile interval if the car was operated under severe conditions.
2. Today the 3,000 mile oil change interval is largely an advertising scam. Everyone who recommends it is someone who stands to profit from the average motorist changing oil prematurely (not that I am advocating that we Mustang owners are average motorists or that our cars are average by any means!). Jiffy Lube wants everyone, from the soccer mom in her minivan to the 4x4 driver who tows a cabin cruiser, to come in every 3,000 miles. So does Wal-Mart, Sears, Quick Lube, and everyone else who stands to make a buck off an unneeded oil change. Besides, there's always the angle for those businesses that perform automotive repairs to use the opportunity of having the customers car on the lift to identify all of the other work (genuine or otherwise) that the car needs... And, how many of us have seen dealer service departments that recommend maintenance at an interval far shorter than what's in the owner's manual? They usually try to tell you that it has to be done that way to preserve the warranty, which is total BS. As long as you can show that your maintenace has been performed in accordance with the factory-recommended service schedule, they cannot use this to base denial of a warranty claim. Sorry if I went overboard about this, but being in the military, it really sets me off when less than honest auto service &/or repair businesses (including dealers) take advantage of our young servicemembers, or even more so their wives when they are deployed, by overcharging or performing unnecessary repairs.
I seem to recall that the 66 Mustang 289 Coupe that my family owned when I was growing up (and that I not only learned to drive in, but performed my first-ever unassisted oil change on) called for a 5,000 mile oil change interval.....
Having said all that, I still change mine somewhere between 3500-4000 miles, but do so largely because I have the time,facilities and inclination to do it myself. Besides, I think it was ingrained in me during the point in my life when I was a starving, VW Beetle driving college student.
If I ever reach the point where I am at the mercy of the quick-lube / automotive service & repair industry for oil changes, I will probably let the interval slide to 5,000.