To make a project more permanent...could one pull out the atmega chip from the arduino (the older ones anyway) and solder it onto a perf board?
Would it be as simple as grounding it and powering it and then connecting whatever sensors you have to its pins?
No. You will also need a 16 MHz crystal oscillator and a pair of capacitors. OR, a 16 MHz resonator. OR, you can change the fuse settings and use the internal 8 MHz oscillator.
If you are using the analog-to-digital converter you may need a few more components.
And, it's a good idea to include an external pull-up resistor (usually 10K) on the RESET pin.
There are some alternatives to consider...http://arduino.cc/en/Main/ArduinoBoardMinihttp://arduino.cc/en/Main/ArduinoBoardProMini
Or maybe something like this...http://shop.moderndevice.com/products/rbbb-kit
Or my personal favourite...http://www.pjrc.com/teensy/
would that work?
Once you work out how you will clock the processor, yes.
Stock: 45,671 Can Ship Immediately ... Yowsers! I wonder how long those will last?
Sorry, got a bit sidetracked. Yes, those are the correct part.
could one use the arduino board as a programmer like that?
OR, the Arduino can be used as a programmer like this (search for "Circuit (targeting an AVR on a breadboard)")...http://arduino.cc/en/Tutorial/ArduinoISP