Lovely question.
My primary reason for getting a battery-electric is ecological -- wanting to get off gasoline. (You can add peak oil, with potential massive gasoline price spikes, and foreign wars to the motivations for wanting to get off gasoline, but for me carbon emissions are reason one.)
The secondary reason is low maintenance. It's not even the money, though that's nice; I just forget to do all the various and sundry maintenance tasks on my ICE (change from summer to winter oil? huh?). Nice to just be able to forget about half of them. For similar reasons, I want something which will last a long time just so I don't have to think about replacing it.
The next question is, why a Model S rather than a different battery-electric? I've been looking for a suitable battery-electric for several years, but I've managed to talk myself out of all the others because they had fatal flaws:
(1) I don't have the time or energy or interest in tinkering to do a conversion (plus see reason #6)
(2) I live on roads which are too fast to get a "neighborhood electric vehicle"
(3) I drive too far, too often to get a Nissan Leaf (especially considering that they don't have thermal battery management yet)
(4) I need more seating and cargo capacity than the Roadster (we routinely have 4 people plus baggage), and I don't like convertibles anyway
(5) I don't trust the car companies which haven't actually produced cars yet
(6) I want something with really good quality and safety standards. The low center of gravity is very attractive in this regard and Tesla has a good record with the Roadster.
(7) Being quite allergic to polyester, I generally shouldn't get cloth interiors, which rules out a lot of "low end" cars anyway. Bleah. I've actually been emailing Tesla about interior materials because I need to know as soon as possible if I have to wrap or replace the floor coverings.
Why a Signature? First, because I had the cash for the deposit and it was earning 0.01% interest without an attractive (to me) alternative investment. Second, because I want to get off of gas ASAP rather than later. It was a bit of a nasty to realize that the Signature requires the 300 mile battery (I only need the 230), but I realized I was willing to pay a huge premium to get the car sooner rather than later. Which is probably irrational, but I really really want to get off of gasoline.
In contrast, why does my *fiancee* agree I should get a Model S Signature? Primarily so I'll stop moaning "I want my electric car", which I have been doing for several years now. Others may want to try that with their significant others.
The other benefits of the Model S are just bonuses for me.
Finally, my goal when choosing an exterior color was to make the car stand out enough that people will come up and ask about it, so that I can then EVangelize.
I've been slightly frustrated in this by the available choices. But I do have a couple of people who I expect will want Model S after they see mine.