My phone in particular had gotten to the point that it would lose a full battery charge in under four hours, without me even using the phone!
Rather than paying for an entirely new phone (EDIT: OR PAYING APPLE $87 TO REPLACE IT FOR ME), which is what Apple and/or Google would have no doubt wanted me to do, I chose to pay the $7 on Amazon for a replacement battery.
I received the battery, followed directions via a downloaded pdf, and as I was putting the phone back together, noticed a MAJOR FLAW in the directions.
They don't tell you how to reconnect the camera ribbon cable to the main board.
It's nearly impossible to do this without adding at least five more steps, which is perhaps why they just skipped this in the directions entirely.
And if you're like me, you put your phone back together only to find that the camera no longer works. Whatsoever.
If you were following those directions, by the way, the "Reconnecting the Camera" step should be right in between step #s 14 and 15. How convenient of them to omit such a vital step.
After a little fidgeting and poking around with a screwdriver, I discovered the remedy:
BEFORE putting the main board back into the phone, remove this screw (marked with a "1" in the picture), along with the small metal brace that the screw is holding down (click to enlarge):
The camera itself is the boxy piece of plastic and metal that is being held in place by the screw and its bracket, highlighted in the previous picture in a red square. The camera is about 1 cm x 1 cm x .6 cm, and is easily lifted straight back out of its brace with the prying tool that comes with the battery.
Which you should do now, of course, if you're trying to reconnect the camera.
With the screw and brace removed, main board and camera in place (click to enlarge):
Now that you've got the main board and camera both loose, you can quite easily connect the two via the camera's ribbon cable and surface-mounted connection interface.
The easiest way I've found to put everything back into place is to slide the main board up and under this tiiiiiny little plastic brace, meant to hold the main board in place and marked in a red rectangle in the picture below (click to enlarge):
Once you've got the main board situated correctly, you can (carefully) slide the camera straight down back into its brace and screw it down with the metal bracket.
From there, screw all the screws, connect all the connectors, follow the directions, and enjoy your brand new battery in your old iPhone 3GS, complete with working camera!