Set a timer or alarm
Whether you're cooking dinner or laying down for a power nap, just ask, "Alexa, set a timer for X minutes." If you have her in the bedroom, you can also turn her into your de facto alarm clock, e.g., "Alexa, set the alarm for 7am."
Explore Easter eggs
Alexa's abilities are constantly expanding, and like Siri, you can have some fun with her. Thanks to Echo users with way too much time on their hands, there are several resources dedicated to logging all of her weird and wonderful Easter eggs.
Keep tabs on the newest stuff she can do
Thanks to Amazon's Skills Kit, which allows outside developers to create custom commands, Alexa now responds to over 1,000 different third-party skills, introduced by big companies like Campbell's and Fidelity (who've added commands that will dig up dinner recipes and current stock prices, respectively), and intrepid developers alike. To stay up to speed, scope out the Skills tab under Settings and refine by "Newest Arrivals."