Man, I struggle with that too. I will most of the time come up with a tune in my head, write some lyrics for it, mess around with it for a while, just to realise it sounds exactly like a song I listen to on a regular basis.
I think it's all due to the "contamination" with the music we like, because we have the tendency to listen to music differently than regular people (like really listen, not just hear) and songs somehow stuck with us on a subconscious level.
What I found works for me is clearing my head space completely prior to the writing process, maybe doing some light meditation to quiet my mind and clear out any possible influences. What also works is disconnecting yourself from music for a while and maybe write songs in days when you haven't listened to anything else.
I'm sure you'll find your own ways of staying original. When it comes to music, everything's been done before, but the stories we tell through it are what gives it an original twist.