Do the samurai still exist today?

The samurai warriors no longer exist. However, the cultural legacy of the samurai exists today. The descendants of the samurai families also exist today. It is illegal to carry swords and arms in Japan. That is why the samurai cannot exist today.

The descendants of the samurai families do not say "I am a samurai." This is because Japan is a peaceful society and it is strange to say I am a samurai. The descendants of the samurai families have ordinary jobs:
The current head of the Tokugawa family: Tsunari Tokugawa (an employee of a logistics company Nippon Yuusen).
The current head of the Shimazu family: Nobuhisa Shimazu (President of a tourism company).
The grandson of Oda Nobunaga: Nobunari Oda (a famous figure skater in Japan).

What is a samurai?

Samurai on horseback, wearing armor and horned helmet, carrying bow and arrows. circa 1878 or earlier Samurai on horseback, wearing armor and horned helmet, carrying bow and arrows. circa 1878 or earlier

The term “samurai” stemmed from the Japanese word “saburau”, which was taken from the Chinese term bushi or buke, meaning “to wait upon”. These terms were originally used to refer to people who served “in close attendance” to nobility
In that aspect, the samurai were men and women who were closely associated with upper and middle-class members of the warrior caste who served their corresponding lords or “daimyos”, and clans as officers and experts in military tactics and strategy.
Samurai were the military nobility and a part of the warrior caste in feudal Japan. The history of the samurai started about the 10th century in feudal Japan when they served under the daimyo or landholders, up to their abolition in the 1870s during the Edo Period. 
The samurai were well-paid by the daimyo and were given high prestige and positions in the estates, giving them managerial experience and extensive education. So they weren’t just an elite class of highly trained soldiers, but they were also considered nobles, and scholars at the height of their power. 
Oftentimes, whenever the samurai were represented in modern media, they are seen wielding a sword such as a katana, and a shorter blade. However, being of high status gave the warriors access and ability to brandish several other kinds of weapon, their expertise being the bow and arrow, which are often used on horseback, and of course, the katana.
There are many well-known and famous samurai, three of which are the Great Unifiers which are discussed in the later parts of the history of Japan. Foreign-born samurai also existed, from people with unknown ancestry to ones who served under a samurai.
samurai & ninja museum samurai & ninja museum

Today, there are many samurai exhibits and museums all over the world and Japan where anyone can have unique experiences such as trying on samurai armor and sword training. One such place is the Samurai & Ninja Museum in Kyoto and Osaka.
The Samurai & Ninja Museum Kyoto is a leading samurai museum in Japan that offers a variety of experiences that inform and educate visitors on the history and relevance of samurais and ninjas in Japan. Some of these experiences will range from sword cutting, historical tours in Kyoto, and a crash course on ninja training.