This is one of my new favorite services, and it's also available as an app for iOS or Android, as a web app for Chrome, or in the browser on your computer. Unlike Pandora, Songza has pre-made, curated "channels" (aka sets) which you can browse as genres, moods, activities, or decades. Each of these sets will have from 3 to more than a dozen playlists, and each of those playlists will have 50+ songs.
Songza also has a "Concierge" that will suggest music for the time of day, and offer a half-dozen or so categories in each selection, with three playlists in category. One thing I like about Songza is that I hear more and different than in my Pandora channels. Songza has just been bought by Google and is free and ad-supported, but the ads are just a pre-roll video before the channel starts, and an ad banner at the bottom of the app. If you want to get rid of those and have more skips, Club Songza costs 99 cents per week ($3.99/mo).