Verizon currently has the extended battery for the Stratosphere on sale at 50% off ($24.99 instead of $49.99) online and at local Verizon corporate stores (call the store before you go, though). There are informative discussions about it here: http://forums.androidcentral.com/samsung-stratosphere/145059-extended-battery.html and here: http://rootzwiki.com/topic/9064-standard-vs-extended-battery-updated-1262011-920-pm-cst/.
There are pros and cons to this battery. The biggest, pro, of course, would be longer battery life. It's a 3000 mAh battery, compared to the stock 1800 mAh. I only got mine today, and it came with about a 40% charge, so I can't comment on how long it lasts yet personally. The second of the two links above has some discussion on that.
The major con is that it is twice as thick as the stock battery, and of course heavier as well. This means that the stock battery cover will not fit, so Verizon throws in a new, customized back cover when you buy the extended battery. The whole phone thus becomes thicker, which then means that standard-size cases, holsters, dashboard mounts, desktop dock, etc., won't fit either (at least, that is the report that I've seen).
However, when I bought the battery at a Verizon store, I asked about cases (I don't use one now, but I might want to), and they did have one available that was made for the larger form factor with the extended battery. I wonder if maybe more will become available as more people buy the battery.
My findings so far: At this price, I think it's a great, great buy if your use of the phone is such that you need an extended-life battery. It definitely changes the feel of the phone. It adds some weight and bulk; but IMHO this wasn't a light phone to begin with. I think it fits my hand better with the extended battery, but of course that's going to vary from one person to another. I also think it makes the physical keyboard more solid and stable for typing, which is a definite improvement. Unless you're a riverboat gambler type, though, I'd recommend buying at a store rather than online, so you can get the feel of it before you put your money down.
I'll report on battery life experience after I charge it up tonight and use it over the next day or two. Has anyone else tried out this battery?