Wrestling is one of the oldest olympic sport which was removed from olympics since 1904.
I need to know,
What is the oldest olympic sport that continued till now?
The only summer sports that have never been absent from the Olympic program are athletics, aquatics (the discipline of swimming has been in every Olympics), cycling, fencing, and gymnastics (the discipline of artistic gymnastics has been in every Olympics).
The only winter sports that were included in all Winter Olympic Games are skiing (only nordic skiing), skating (figure skating and speed skating) and ice hockey. Figure skating and ice hockey were also included in the Summer Olympics before the Winter Olympics were introduced in 1924.
With regards to those last two:
user1564's answer covers the modern Olympic games. However, some of the sports that are included in the Olympics today have their roots in the Olympic games of ancient Greece. The sports from those games included:
Other than Pankration, all of the other events in some form were included in the modern games. Many people are upset at the removal of wrestling because it is one of the few sports that traces back to the ancient games.