Most car engines are built way down to a budget, huge lumps of metal with a "down to a cost" manufacturing process.
It really depends on the car but in most cases on a standard 6.5K RPM rev limit you find on your run of the mill stuff your making peak power at about 5K RPM and the most efficient change point is at around 5.5K to drop you back into peak power for the next gear. Going any higher without engine modification is only useful when your trying to hold onto a single gear on a section of track road where changing up will mean you need to change back down again immediately. Racing at Brands Hatch is often like this with some bikes banging it off the rev limiter down from Druids to Graham Hill as a gear change costs more time than you gain in increased speed.
Once you've had head work to flow more gas, better fuel injection system, full exhaust, increased rate valve springs and light weight valves then you might be able to raise the rev limit and with a re-map get more power. This is on most cars/bikes, there are exceptions in either case.
To get more power you are always looking to flow more air/fuel. This can be done by reducing flow restrictions, increasing compression, increasing capacity or increasing revs.