Powering Arduino from 12v 1A linear regulator?

fungus:

Connecting a few of the regulators in parallel allows a few more outputs to work before they all cut out.

Connecting regulators in parallel is bad. Don't do it.

You see, you have to remember that voltage regulators are active devices. That is, they watch what is going on with the voltage and make a decision about what to do with it. If the voltage drops too low it makes the decision to increase its output to raise the voltage. If it's too high, then it decides to lower its output to compensate. Now imagine you have two regulators in parallel. They're both going to be making independent decisions about the same voltage. They'll both decide to raise their voltages or lower their voltages, and the net result will be too much or too little voltage all the time, so they'll then try and compensate again. The two regulators will be fighting against each other to gain control of the voltage, and neither will get control. They'll just be getting in a complete mess.

Connect an oscilloscope up to one of the paralleled regulators, and chances are you'll see the voltage varying massively all the time.

The way to increase the power handling of a linear regulator is to add an external PNP power transistor, but I wouldn't recommend it, since the way to go is definitely with a switching regulator.