I've been trying a couple - Forza and Onefootball, both for following the Premier League (though both can follow other leagues too).
Forza is quite nice as goal notifications are a bit fancier graphically and usually include a picture of the goalscorer, but I have found the live score on the app doesn't properly update the main "big" counter which seems to remain at 0-0 throughout the match. It does still show the latest score just beneath in a smaller font though - hopefully this will be corrected soon. It also doesn't properly "push" goal notifications - you have to set a refresh rate in the main phone app for it to check for goals either every few seconds (which is bad for battery life), or up to every few minutes (which while better for battery does mean you aren't getting those goal notifications as quickly as you might like).
Onefootball seems a lot less buggy and it does seem to do proper push notifications too, but it is a more plain looking app.
I'm still trying them both out to decide which I prefer.