In the above photo the size of the replacement, extended battery is shown next to the 3DS.
The Short Version: I purchased a 5000mAh Li-on Extended Battery for the Nintendo 3DS for about $20 via Amazon. It significantly increased the charge capacity of the device. I found the larger bulk of the entire system to be an acceptable trade-off for the extra play time this battery provides.
This week I decided it was time to replace the factory battery in my Nintendo 3DS. It wasn’t because it failed to maintain a charge but simply because it didn’t last as long as I would prefer. Now, I wasn’t draining the battery from playing games. In fact, most of the time I drained it simply by leaving it in stand-by but not on the charger. However, I also wanted to upgrade the battery because I thought I might begin playing the system more frequently and that it would be nice to not feel tethered to a power cable when I’m at home.