A couple wires, a diode, a 5v to 9v usb adapter, and you are in business. The reason I did this was to make a fish feeder work for at least a week. I was going away and didn't want anyone to be burden with fish feeding.

Supplies:
Usb cable for NXT brick (included in Mindstorm kit)
5v to 9v usb adapter
A 2 amp diode ( thank you Lan01)

Tools:
soldering iron and solder
wire (small size from radio shack)
Phillips screw driver
wire cutters and needle nose pliers

Step 1: Opening NXT

Take out batteries and the four small screws in each corner (Not now but in a future step you will need to pay attention to the little black button in the low middle of the picture). Turn over brick and pull on the white face plate. Might be a little tough but comes straight out.

The board is attached to the screen by 3 items. 1.) Two screws one on each side of the screen. 2.) The 10 solder spots. If you just pull up from that spot it should come right out but be careful because the side with the speaker has (3.) 2 wires that do not separate. So fold the screen over on its face. You can put something soft down so as if not to scratch it (as you can see in the third picture I did not. Nothing was scratched but better safe than sorry).

Step 2: Inside Case

Now its times to take off the two dark gray ends. The battery pack and the main board is attached by two points of solder but only on one side. In order to pull the pieces off you must pry open the board and battery pack at the opposite end they are attached. The two gray ends are held there by two small plastic pegs. If the gap is big enough you can slide them right out. Remember the little black button in the battery case. If you separate the board from the battery pack this will most likely fall out. This is fine it is really no big deal. Just make sure not to lose it. To put it back in later I just used needle nosed pliers.

Next take two wires cut them decently long and have the diode ready. If you can see from the picture I wedged a battery in between the board and battery pack to give me room to solder.
The bottom of the usb port has 4 major solder points. The two closest to the larger side is the power.
In the picture the wire with the knot is the + (do not put a knot in the wire but a black mark because you will be routing these two wires into a small hole).

After you solder the two points run the wires into one of the screw holes(same screw holes that hold the face plate to the battery pack) to the side of the board that has the screen on it .

Step 3: Final Stretch

Alright the wires should be sticking out of the screw hole closest to the usb port. Now stretch out the wires to go to the two battery ports on the edge of the board. The terminal on the left is + and the terminal on the right is -. Now keep in mind you have to solder the diode (Thank you LasVegas) to the positive wire. The diode has a indicator to show which way you want the power to go. You want the indicator pointing towards the battery terminal. After soldering I electrical taped where the wire met the diode. I next laid them out and cut to where the end of the diode met the battery terminal. The solder on the battery points are thick but if you are patient and let the solder melt. The diode will have no problem plying itself.

Step 4: Finishing Touches

The face plate needs a slight modification since one of the screw holes have wires in it. I just trimmed the one peg a little shorter with wire cutters and it fits together fine. Just make sure you cut the correct peg. In the picture it's the closest peg on the right that I cut.

Putting it back together is no big deal. Just put the correct dark gray pieces on their corresponding sides. The side with the soldered wire on the bottom might be a little tricky but be patient and if you made you solder and wire too exposed to fit the piece. Just take a deep breath, realize you are almost there, and redo it. After the sides it is time to put black the little black button. Now fold the screen back over and push it into it's 10 slots. Screw down the two screws that hold it to the board. Throw the face plate back on and screw it back together.

Step 5: The Moment of Truth

Take the 5v to 9v usb converter (http://www.seeingwithsound.com/usb_powersupply.htm) and plug it into your computer's usb port. Take the usb wire and plug one end into the converter and the other end into the NXT brick. With no batteries in it hit the start up button. Congrads!!!! You have a NXT brick that runs on batteries and usb power. If it did not work start trouble shooting. Open it up again and make sure the solders are good and tight. If that seems all good and well make sure the diode is correctly pointed towards the battery terminal.