Even if you decide not to sign-up for Apple Music, you can still get the experience of Beats 1 as a music discovery tool. It won't help you listen to the exclusive interviews or get to know the station's DJs, but it will give you access to their playlists.
Tweeting Beats 1
Developer Callum Jones created the automated Twitter account Beats 1 Plays, which tweets out every single song as it hits the "airwaves." In my experience it took just a few seconds for a song playing on Beats 1 to hit the Twitter account.
Twitter users can just follow the account or watch it update live. Non-Twitter users can visit the account's webpage, but won't see receive the live update feature.
This is also a great tool for Apple Music subscribers who missed the title of a song they were grooving too and want to make a note of it for later. As this is an unofficial Beats 1 account, it's not clear if Apple will try to have it taken down.
Beats 1, now on Spotify
A collaborative Spotify playlist called Beats 1 Tracks relies on a cadre of Apple Music enthusiasts to update it with recently played tracks. This is not the best solution since the playlist is really long. It's better for getting a flavor of the station rather than an up to the minute track list. The playlist is at the mercy of Spotify's catalog, so if a song is missing it may be swapped for something else or skipped altogether.
It's also not clear how long the playlist will continue to be updated, but it was active at this writing.
Apple Music is part of iOS 8.4, and available to Windows and Mac users by downloading iTunes 12.2 and then visiting the For You tab in the music section.