Oh boy, great question. Over the last couple of months, I've been writing apps for a single user: me. Here's what all I've built so far:
1. A custom twitter client
I feel like tweeting whenever I get an insight so I post a tweet several times a day. But I whenever I used to tweet, I'd get pulled into an endless stream of notifications and timeline. So I wrote myself a client that does only one thing: posting of tweets. It has no timeline, no notification. In case you want to use it, it's hosted on https://tweetaway.herokuapp.com/
2. Site-specific search (along with Google)
I find great content on HN, so I built myself a stupidly simple website which opens up Google.com and site:ycombinator.com +keyword whenever I search. Using it, I've come across so many interesting threads that I would have never discovered. E.g. when I searched for entropy, I came across this gem: https://news.ycombinator.com/item?id=14709896
You can access it at https://dualsearch.glitch.me/ (you'll require a Chrome addon to modify Cross-origin headers because Google doesn't open in Iframe)
3. I miss my cat at work, so I built a Chrome plugin that shows an icon of her + a funny one-liner https://chrome.google.com/webstore/detail/orbit-the-cat/fjni...
4. Last weekend, I wrote a twitter bot that retweets my old tweets that got many retweets (to resurface them in US timezone, because at that time I'm asleep)