If you sign into your Spotify account there are a number of places you can find playlists to suit your musical tastes.
If you go to the "Browse" section, there is a tab called "Top Lists". This will give you the most popular songs on Spotify by genre - for example "Top 100 Hip-Hop songs".
The next tab along is called "Genres & Moods". This is my favourite part of the site for lists, as it breaks things down by genre, and then gives lists for specific things, so you can find exactly what you want.
For example, if you click on "Country", you'll then get access to lists such as "Pure Country", "Country Drive", "Country Duets" and so on...
You can also view lists of any Spotify users that you follow by going to their profile and clicking on "Public Playlists". This allows you the option to "follow" a playlist so that you are alerted if new songs are added to it.