Craig, I was a general contractor for years and did a lot of construction under the UBC (Uniform Building Code), which was the standard for most state and local building codes in the western part of the country at the time. According to the UBC, structurally you could build most homes or commercial buildings with 2x4 studs spaced 24 inches apart, as long as they were one or two story buildings. No one did, though. The 16 inches you mention was the standard spacing for exterior walls, interior partitions, ceiling joists and roof rafters anyway (although trusses were usually 24" on center).
Partly that's just for convenience -- because plywood, drywall and other sheathing materials come 48" wide. Being able to span four framing members with a full sheet instead of three gives more nailing for sheer strength. It also provides more fastening points, for everything from electrical outlets to cabinets. Also, it usually results in less waste. For example, say the length of a particular wall is 12 feet and three inches. With 24" spacing, you'd wind up with a cut-off 21" wide -- and probably toss it. With 16" frame spacing you'll be able to use most of that 21" piece, and only throw away a 5" strip.
Another benefit is the fudge factor 16" on center provides for structural strength. With studs 16" on center, there's a lot less worry about the wall not being strong enough if some idiot plumber or electrician gets carried away with his Sawzall and drills.
By the way: since I've gotten out of the business, the standard size for exterior wall framing has changed from 2z4's to 2x6's. That isn't because it makes the walls stronger (although it obviously does), but because it makes more room for insulation.