YES! Your original ticket is still valid and is yours to keep. Remember, it may be automatically rebooked by your original airline. Feel free to seek a refund from the airline or keep the ticket as a back-up.
If you rebooked the outbound leg of a round trip, you must contact the airline and let them know that you still plan on taking your original return leg. For more information, feel free to ask firstname.lastname@example.org.