ultra-low tech version (over an open flame in the woods for instance)
1x keggle to brew in
1x cotton voile as a grain bag
1x corona mill to mill the grain
2x fermenter buckets for a 10 gallon batch, to ferment in
2x airlocks
1x auto-siphon to move water and wort
1x hose for auto-siphon

for the electric version (recommended for a city)
4x heat sticks with GFCIs to heat the sparge and mash water and do the boil
a long stem thermometer

for the high-tech version add
1x computer
4x SSR cords to turn the heat sticks on and off remotely
5x JeeNodes (you could probably do it with just 2 jeenodes, if you hack the code a little bit)
5x AA Power Board (or as many as you have jeenodes but if you want to save some money in the short run you can run your jeenodes on 9 volt batteries and hook-up wire)
1x Temperature sensor to measure water and wort temperature
1x JeeLink which allows your computer to talk to the Jeenodes
1x USB BUB II with mini-USB cable to program the JeeNodes

X lbs malted barley
Y oz hops
1x packet yeast
a water source (the cotton bag and corona mill are for all-grain recipes)