UpNext is a tweak that allows you to queue up songs in the default Music app in a similar fashion to iTunes on Mac. It works on all devices running iOS 8.1.
Swipe left on a song and two new options will be revealed: "Play Next" and "Queue". "Play Next" will add the song to the front of the queue, "Queue" adds it to the end of the queue.
To manage your queue, go into the now playing screen and tap the top right button. It'll bring up an interface where you can manage your queue. You can rearrange songs by dragging, remove songs from the queue, and skip to a song by tapping on it.
There's also a notification centre widget that displays the up next queue. As with all new widgets on iOS 8 it isn't enabled by default; you'll be able to find it by pressing the edit button at the bottom of the today view in notification centre.
The widget is hidden when there's no queue so it doesn't take up space for no reason, that means you won't see it straight away when it's added to notification centre. You'll only be able to see it when there're items in the queue.
When viewing all albums by an artist, there's a new button in the top right of each album header. Tapping it brings up the popover shown in the fourth screenshot, which allows you to queue the whole album right from that view. Search results can now be queued in the way you'd expect. Fixes a bug that caused unexpected behaviour when you wanted to play a group of items next.