I have the little one, but I didn't buy it. I found sitting on top of the trash bins in our apartments and had no idea what it was, so I took it home.
At first, I used it for laughs by saying random phrases to get a response. Like "hey Alexa, do you know Hal?".. she responded something like "yes, but we haven't spoken since that thing happened"
There are tons of little easter eggs. She also can quickly do conversions if you are cooking, like "Alexa, how many teaspoons are in a cup" or whatever. Oh yeah, and ask her any math problem. The best place for this thing is in the kitchen in my opinion.
For me, the thing that I have found most useful is using her as a timer, or alarm. "Alexa, remind me at 2pm tomorrow to meet Alex.". That has been really helpful, actually.
But the most fun we have had is this sort of thing: "Alexa, remind Amanda at 3:45pm that she sucks". This war has been going on for a while in my house.