My guess is that nobody starting using the BC/AD system for awhile after Jesus died, but what alternative calender systems would they have been using at the time? What was the base year?
There's always room for discussion, but perhaps the section Calendars and timekeeping from our FAQ will answer your inquiry.
While FAQ is awesome and should provide you with an answer, just like Mictlantecuhtli said, I would like to point out specifically, that 0 AD does not exist. The concept of "0" had not arrived in Europe by the time the Christian Monk Dionysius Exiguus tried to calculate the time of Jesus' birth. The calendar goes from 1 BC to 1 AD, skipping 0.
Also: Jesus didn't die in 1 AD (your post implies that you believe that. If you don't, never mind). 1 AD marks the birth of Jesus, not his death.
A popular one through (fairly) modern history is the Hebrew calendar. Though it's more convenient to now use the Gregorian calendar, the Hebrew calendar was used for thousands of years.
The Hebrew calendar is a lunisolar calendar based on sunrise and sunsets and evenly divides the hours in a day by 1/12 of the period where the sun shines. The calendar is currently at AM 5776, which represents roughly 5776 full years past it's start date, the creation of the world and the creation of Adam.