I started using a stand with both smartphones and tablets about two years ago, and it's made a world of difference.
The first problem is one I think most people face on a semi-regular basis: I would forget where I put my phone.
For better or worse, I used to leave my phone on window sills while still living at home. This lead to me frantically running around the house with the home phone in my hand, trying to hear the my iPhone vibrate — I always kept it on silent.
Tired of all the running around, I bought a couple of phone stands and kept them in my bedroom and the computer room. When I left one of those rooms to do something around the house, I would put the phone in a stand, where it would finally stay put. As silly as it sounds, this was a game-changer for me, and I didn't spend nearly as much time searching for my stuff.
My second problem was more niche: I was trying to use my iPad for more productivity-focused tasks, and needed a way to prop it up. Typing on an iPad's software keyboard works well, but it also covers up half the screen, which isn't very efficient.
I was also doing some design work at the time that required me to make subtle changes to images on my computer, and view them on my iPad. It became tedious to pick up and put down the iPad after every change, so I stuck my iPad on a stand, and positioned it so I could just glance over after every few seconds.
You may have overlooked it in the past, but having a phone and tablet stand is one of my most important tech accessories. If anything I've written rings true for you, I can't recommend one highly enough.
I've moved on to using the exact one we feature on our website (because its quirky, fun, AND it works like a dream. You can pick one up here: Gooseneck Phone Holder. Best investment ever.