As a traveler, I especially like maps that I can edit to mark where I've been. There are lots of these. Of course, there are physical ones that you can hang, but I want to focus on the digital ones online and on iOS. None of them satisfy me, by the way, so I guess this is a sort of critique, and a manifesto of what I want in a map.
Let's start with Google Maps. This is an obvious resource - simple, free, straightforward and pretty great. Above is my personal map of cities visited as of mid-2018.
If you google something like "map where I've been" or something like that, one of the first hits is this interactive visited countries map - a basic mercator map divided by countries. You can easily mark the ones you want, and even change the color of each value (marked, unmarked, ocean). Above is mine, as of early 2018. I like the look of this.
Even though the mercator is a reviled map projection among cartographers, it is quite helpful for most travelers because it enlarges Europe. (It distorts everything away from the equator, as obviously exhibited by Greenland - as it happens, Europe is quite north, so it benefits from this projection.) I love that I can alter the color scheme of this. But I really dislike that I'm limited to the official country designations of the UN.