I've used selenium pretty extensively since 2007. There are a lot of good examples out there, the docs are good, and its written in a very extensible way, so I've always been able to find a way to accomplish what I'm trying to do. (anything you can do in javascript!)
Ways I've used it:
1. create basic smoke tests that test the happy path of an app, to be run after a new deployment
2. use the Selenium IDE firefox plugin to record a 'how to recreate a bug' scenario, and attach it to a bug report, greatly reducing the amount of time to document and explain the steps it takes to get a bug to happen.
3. when integrated into the app, with some customizations, allow a QA user to dynamically choose elements to feed the selenium test (2 adult, 1 child, ord-sfo, round trip, with refund)
4. to fill in forms I don't want to fill in again (chili's and home depot receipt surveys)
5. Setting up accounts, re-initializing my stupid vonage motorola router that loses its settings if the power goes out
Selenium is great, and has gotten people thinking about how to test the app and drive it the way that the user experiences it.
There are certainly some draw-backs, and other tools that should be explored, but I think Selenium is part of a 'balanced testing diet'.
Is its common use case to enable testing for people who aren't normally writing them, reduce total number of tests maintained for people who are writing them, or for writing additional supplementary tests to guarantee a higher confidence in interface functionality?
edit: context is prototypical M-V-C python or ruby web app development
Yes to: "tests to guarantee a higher confidence in interface functionality "
Selenium should be part of a complete suite of tests (unit, component, feature/acceptance). Selenium's design goal is a "for developers, by developers" feature testing tool -- a browser automation API with bindings for all major programming languages. Classic "perfect user" is an open-source and agile loving Java/Ruby/Python/C#/Perl/PHP programmer.
However, because of the Selenium IDE browser extension for Firefox and its "record/playback" feature, Selenium is also commonly used by people who don't normally write lots of tests. Even though those users are not "real" programmers, there's so many of them... So I try to be nice to them most of the time. :-)
This is absolutely why I love hackernews. I mean really...how often do you have a question about a piece of software and the creator jumps right in to provide some insight!?
Disclosure: I was working at Thoughtworks with Mr. Huggins when the first version of Selenium was released. Also, I was the very first user of the Watir browser test tool, and at one time I was fairly active in both communities. I have been familiar with these tools since the beginning of their existence.
edit: context: one of the bundle inclusions is selenium cloud testing (sauce labs)