I just ordered a Google Home (an impulse buy) to go along with my Nest doorbell, Nest thermostat, and Chromecast devices. (Yes, I do own Google stock. Why do you ask?) If you own any of the home smart devices (I’m not sure exactly what they’re called), what do you ask of them?
Alexa maintains grocery and other shopping lists; “Alexa, put eggs on the shopping list” is probably the most common thing I do with it.
I also use it to listen to the radio & podcasts quite a bit.
Less common but becoming more common: ordering things from Amazon. We have a handful of perishables we get from Amazon, and I find myself saying “Alexa, order more Honey Stingers” pretty often lately. This is happening a lot more now that I have an Echo Show - without a screen to double-check that I ordered the right thing and the price is correct and all that it was not nearly as efficient.
We also occasionally ask questions of it. “Alexa, what’s 134 divided by 28?”, “Alexa, what year did the movie ‘The Matrix’ come out?”
I also bought a bunch of smart plugs to use with my Christmas lights and had Alexa wired up to turn them on and off. “Alexa, turn on the Christmas lights” was way easier than running around to the 6 separate light displays and doing it manually. Now that it’s not the holiday season, we don’t use that nearly as much.
I ask her to play music from my Amazon Prime list. Or what the temperature and/or weather is outside. And set an alarm for the morning.
This kind of thing. And “what time is it?” and “when is the next low tide?”
I would say we underutilize its capabilities.
Music or shopping lists.
Lots of times when I’m watching TV, I’ll ask it how old an actor is (that I’m watching on the TV), or what years did a show run. Or what time does “X” show come on.
I also control the lighting with it.
Echo Dot. Thought it would be useful but not so much.
Echo Input. An Alexa device that just connects to your own stereo/whatever. Got this for Mrs. FtG. She tells it to play a type of music and it plays music. It
does all the usual Alexa stuff. A good economical start to the Alexa world.
Dash Wand. The least powerful of the Alexa stuff. Battery operated, push button use only. (So can’t play music, do reminders, etc.) I have it next to my chair and use it once in a while while doing crosswords. But it isn’t really smart enough to answer most questions.
Chromecast. I just don’t like this. Staring at your phone while trying to FF or whatever a video, etc. Basically only used when Mrs. FtG’s team’s game is on Facebook so I cast it to the TV.
I have a Fire TV Stick and a regular Fire TV. The latter has an Alexa remote. I see no use for it. (I run Kodi on those most of the time anyway.)
I got a Google AIY for Raspberry Pi for practically nothing. Never got it too work. (Both the included pamphlet and Google’s help pages did not correspond to the actual web pages at all. :()
Chromecast works with a computer as well.
I have an Echo in the living room and an Echo Dot in my bedroom. I live in a small one-story house, and I have smart plugs on the six lamps I use every day. When I wake up I tell Alexa to turn on all of them. When I go to bed or when I leave the house, I turn them off.
Something that I use called Alexa Guard works like this: When I leave the house, I say, “Alexa, I’m leaving.” The Echo listens for the sound of the smoke alarm and for breaking glass. If it hears that, it sends you a recording of the sound, so you can decide what to do about it. When you get home, you say, “Alexa, I’m home,” and it turns off. You get a text message each time to confirm.
I also use a skill called “Burglar Deterrent.” When you enable it and tell Alexa to play it, the Echo produces sounds that make it seem that someone is home. It will ask you what time of day and what room. So you can get kitchen sounds, music, dog barking, someone stirring a cup, coughing-- all normal background noises.
I use a skill called, “Relax My Cat,” which is some casual noodling on a flute and possibly a harp. It sounds kind of random, i.e., there are musical phrases and some key changes, but no lengthy melody. I’ve listened to it so many times, it doesn’t sound random to me any more. It’s perfect background “music” for falling asleep, napping, and just relaxing. I don’t know if it relaxes my cat, but it certainly works magic on me.
The shopping list is one of the best things. You remember while you’re doing something that you need paper towels, so you call out, “Alexa, add paper towels to my shopping list.” Then when you get to the grocery story, you look at the Alexa app on your phone and the list is there. No looking for a pencil and a piece of paper and then remembering to take it to the store.
I don’t do any voice ordering-- I have that feature disabled.
Setting reminders is another great thing. Okay… gotta run. Alexa just reminded me to turn off the water in the front yard! Thanks, Alexa! (When she reminds you verbally, you will also get a text reminder on your phone.)
I ask Alexa the weather almost every day.
I play music from my Prime Music collection almost every day too. I have a bluetooth speaker in the shower and pipe Alexa through that when I shower.
Sometimes I have a song in my head that I don’t have in my library, and I ask Alexa to play it. There’s a 50/50 chance that it’s already free on Prime so I get to hear it. Otherwise I hear a sample of it.
When I’m reading Rolling Stone and they mention a song that I’d like to check out, or just hear what an artist sounds like, I ask Alexa to play it.
Sometimes if I’m listening to NPR in the car and still want to keep listening when I get in the house, I come in the door and say “Alexa play NPR” and it tunes right in to my local NPR station. There’s a bit of a delay so I usually don’t miss any of the story while I’m making the switch.
I used to listen to baseball games with my MLB radio subscription but that feature is not available this year. It was great because I could put on the game and go to bed and it would turn off at the end. Now I’m back to real radio and I have to get out of bed to turn it off when the game’s over.
I use it on occasion to set alarms.
Several people have mentioned “Add xxx to my shopping list”. You don’t need to say “to my shopping list”. Just “Add xxx”.
Now if you have multiple lists (Sprouts, Kroger, etc.) and want to be more specific, you can include the specific list - “Add xxx to Sprouts”, for example.
I never thought of this. That will save me from sitting for 15 minutes in my driveway til the show is over (9 times out of 10, it’s Fresh Air).
Not if the windows are rolled up, it’s not! 
I remember somebody on NPR (during a pledge drive I think) describing good programming as “driveway moments”, in reference to people doing just this.
These sound pretty good, i’m going to have to check them out.
I have Alexa built in to my home theater system, but all i use it for is to turn off the TV. She can’t, for some reason, turn it on. I used to occasionally ask her to tell me a joke, but they were sooooooooooooo bad that I stopped asking.
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A computer works with a computer as well. I.e., if I’m on a computer then I usually don’t need to cast to something else.
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Using a computer to control a cast on another device is not easy either.
In short, once something is playing I like to use a real-button remote to Pause, Play, etc. My eyes are on the screen, the remote is controlled by feel in my hand. So Fire TV devices work like this. Esp. if you have a new remote with volume/etc. buttons or an old one with a Sideclick. (BTW: There’s an app for controlling a Fire TV device. It’s … not pleasant to use.)
My initial understanding of this sentence was: “I just gave an order to a Google Home (an impulse buy) to get along with my Nest doorbell, Nest thermostat, and Chromecast devices.” 
There’s are scripts in the Alexa app that you can customize. I say, “Alexa, start my day.” I get the weather, commute time, stories from Reuters, NPR and BBC, a couple of other things.
I have an Echo Dot. I also subscribe to a $0.68/month service called Sleep Sounds that plays dozens of “white noise” sounds through your echo and, if you subscribe instead of using the free version, allows you to combine 2 sounds at the same time. Well worth the cost
Other than that, Alexa gives me the weather, plays a workout playlist I’ve curated, tells me if TV shows were renewed or when the next episode is, and gives me reminders. Oh, and meows at my cat!
I don’t really use mine (Alexa built into a tablet), but something I know a lot of people do that I’ve not seen mentioned is use it for a kitchen timer. You can set it even when your hands are busy doing something else, and without pressing fiddly buttons. You just say “Alexa [pause] set a timer for [time].”
It’s the one feature I think my mom may use with Alexa on the tablet I just ordered her because hers died. She’s constantly asking me to set a timer for her, because she hates fiddling with the buttons on the microwave or oven.