In my household, we never thought we would have a need to subscribe. Back when it was $79/year (US), we were like "don't need it; we order things once every couple years". It went to $99/year, and we still waited, although it took us until 2015 to really start ordering things more frequently (once or twice every 3 months or so). Still wasn't worth it, until my mum said last year "Let's just try it and see what happens" because we have family that uses it and raves about it.
One neighbour uses her friends' household membership, even though the friend is in New York and she's in Florida. So as long as you have a valid email, household memberships can be beneficial if you want to "share the wealth". My mum is listed under my household membership, so she's got her own private account and it allows her to use all the Prime benefits without worry. And we are in the same house.
In the past year, we've really "gotten our money's worth" with it - between ordering "necessities" (air filters for the air conditioner unit, water filters for the refrigerator) and smaller, lesser needs (watch bands for my knock off fitbit, 2 Autism Awareness decals for my car), we really have utilized the "free 2 day shipping" aspect, so we bit the bullet and paid for another year (it's now $119/year).
With the video streaming, I have a Roku, so it was a matter of signing on to the Amazon Video app. The original content alone, could be worth the wild of people who like to binge watch shows. You do have to be careful though - if it doesn't have the PRIME banner on the upper left side of the video poster, it's a pay video. Even though Prime gives you the option of shows and movies being included in your membership, you can still purchase the video too. I had to explain to my mum that if she is watching something without me, make sure it's got the Prime banner, or I'm getting charged accordingly. That scared her into only wanting to watch when I'm around.. LOL.
We had a cousin who saw a movie on Prime, and told us we need to see it. When I looked at it, it was a paid movie - like, HD=$X and SD = $X. We said we aren't paying for it; we like to be able to watch the "freebie" stuff. But however you want to use it, is up to you.
Like people have said, watching movies and shows depends on your internet speed - whether or not you have issues in viewing. Same goes with streaming music. We've not noticed any issues in our videos, except a few times a year, because our ISP has random problems (and we have one of the lower tiered internet services).
The music player can be downloaded to devices as well, and you get something like 20,000 songs for free versus a paid music account of 50,000 songs. We bought an Echo Dot last month, so we have been streaming the free music on that. There are some songs where it only gives samples, because it's either a brand new album, or it just wants you to go and pay for it. But any album you buy, can be played in the music app.
If you have smart devices, you can download the apps you want - video or audio and be on the go with them. I don't know much about travelling abroad, because I've not used it to that extent (yet).
I've seen an Echo Dot for Kids online, so there has to be a way to add a kid friendly account (like others said, it's a matter of enabling it). I don't have kids, so that's why I don't know anything about it.
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e2a: I forgot to mention:
A "Perk" of Prime is that you don't need to get a massive amount of items to make "free shipping". Meaning, Amazon has a set standard (lately it's $25 as the cut off) to make shipping be free. It's been over $30 too. All total, before tax. With Prime, I've bought single or multiple items that don't make $25 total, but I still am able to get free 2 day shipping. Maybe it's because they were Prime specific items, but I actually checked the watch bands I got - there is no Prime logo on the page (usually there is), but I was able to just buy a pack of 5 bands for $11.99, pay zero tax and zero shipping. I think it's a matter of what you're looking at, and able to find it within affordable range.
I was talking to a co-worker of mine, last week. He is a young gamer, who shares a regular Amazon account with his family. We were talking about Prime, and the benefits, and he said that the family can't really justify the price, even though they do use the site a lot. Since he had just bought a game there, I asked him what he usually spends a year - how many does he buy from the website? He says, "minimum 4". What are the costs per game? "$40-60". Sometimes he'll buy a game and ask his family if they need anything; they'll say no, he'll order. 3 days later, a family member decides they want something. There goes another order. So I said "Look, you buy a minimum of 4 games at $40 each, a year. That's $160. If your parents or sister end up buying something a couple days later, the credit card is going to be going through a vicious cycle of charges. Even if they get little things. For $119 for the year, you've paid that off and then some, in your games alone. Family buying something randomly is an added bonus". He understood, saying he would tell the family, but I don't think they'll go for it.
Essentially, it's all in how much you think you'll shop in the year, added with the options of video and audio streaming. Like I said, the latter 2 are worth it because "old" videos are $15-30 a DVD, especially when you get into full seasons of TV shows. I just finished watching season 1-3 of Mr. Robot; had I bought the seasons to stream, it would have been $59.97. And that's not a physical copy of each season.
Music will be the same way, unless you like physical CDs or Vinyl. Still worth it; I've bought albums where I'll get the CD or Vinyl in the mail, and I'm offered an "AutoRip" option immediately. Meaning, I can download the album, in full, to my laptop and then burn it to a blank CD or put it on my MP3 player.
The options are there. It's a matter of what you want to do with them.