Distance of 78xx/79xx Voltage Regulator to Circuitry

It is inductance, not resistance which is your enemy here, and it only starts to play a role at higher frequencies.

By mounting appropriately sized decoupling caps close to the action part, the effect of this inductance can be negated. I wouldn't worry at all about 15 or 20 cm of twisted wire between the regulator and the circuit, given adequate decoupling.
The 78xx/79xx regulators have their internal gain rolled-off above only 1Khz or so. This means that the worrying about the added inductance of ten cm of wire has little effect on accuracy of regulation, because the regulator already has an intrinsic 2-3 microhenrys in effective output inductance (a side-effect of limited feedback bandwidth)

If you need to mount them a few cm away as described, just don't worry about it. Best-practice in decoupling, as post #4, is very much more important anyway.
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2002-09-25 11:01 am
If your regulators are expected to run hot, it is either due to large voltage difference or large output current, or both.

A two-stage cascade regulator often works well to reduce the load across a single 78xx or LM3x7. These are reasonably durable devices and can handle 400-500mW continuous dissipation without any heatsink at all, in ambient temperatures of 50 degrees or so. This works out to a current draw of 150mA at 3V drop, which is the minimum for decent regulation.

If you need more current, a TO-220 unit is probably not the best choice without some form of external help or a heatsink. If your voltage headroom is higher, consider a pre-regulator. I've used series resistors when the load is predictable and constant to serve this need, but a second chip really improves PSRR.

I've also used ripple eaters (either series or shunt) close to the load and 3-terminal devices near the power supply when the DC voltage regulation is less of a consideration than noise levels. There are quite a few ways to skin this cat.