Is 22-Guage Stranded Hookup Wire the correct wire to connect the Switching Powersupply to RAMPs 1.4? I obtained the following wire 22 Gauge Stranded Hookup Wire from Radio Shack:

Type/Style: AWM/1007
Wire Gauge: 22 AWG
Insulation Thickness: AVE. 0.42 mm
Rated Voltage: 300V
Temperature Rating: 80°C / 176°F    



  Use Limitation: Internal wiring of appliances; or where exposed to oil
  at a temperature not exceeding 60°C or 80°C, whichever is applicable..
  Tags may indicate the following: 600V Peak - For Electronic Use Only.


I'd like to be able to hook up RAMPs 1.4 to my switching power supply with this wire.  Will this work okay?
22awg wiring is good for a max of 7A in this usage case. Your power supply can provide 30A. So it is definitely not large enough wire gauge for good wiring practice -- in the event of a short, you want the PSU's over-current protection to kick in before the wiring overheats. That would mean 14ga between the PSU and board. 16ga would probably cover your actual load requirements just fine, but we need to know a lot more about your printer to say that for sure. 

12v systems need heavy duty wiring, at least on the main supply lines. You can use 22ga for individual power consumers, such as fans, extruder heaters, etc. (No heatbeds.)