Distinct from most of the martial-arts actors today, Bruce Lee's martial arts skills were truly impeccable. He trained hard, and can truly be considered, without hesistation, as one of the world's best fighters. There is no martial-arts actor today that even comes close to Bruce's level of martial-arts proficiency, as well as his skill in fighting. Bruce considers himself a martial artist first, before an actor.

As Jesse Glover, Bruce's first student, narrated:

When people see Bruce, they think about what he's doing in the movies. 
That's not Bruce!  Bruce was completely different.  He could stand six or
seven feet away from you, have you put your hand in a defensive posture,
and tell you he was going to touch your face.  You couldn't stop him or
touch his hand, he would just do it, over and over again. 

From a fight prospective, Bruce was primarily a hands fighter.  He would
close the distance between him and his opponent, and use his hands.  In
the fights that he had when I knew him, that's exactly what he did.  He
never kicked.  He closed the distance and punched.  When you see him in
the movies, he's doing a lot of kicking and wide circular movements.  If
he just closed on his opponent with a straight blast and the guy dropped,
people would say, "What was that?"  Nothing spectacular about that.  But
that's the way Bruce fought.  Instead, people wanted to see Bruce kick
high and do the impossible.  It looks more fancy. 

...

The day I brought Ed in (Ed was my roommate.  He was a real good boxer,
judo practitioner, streetfighter, and a real tough guy to read.  He was
very quick and could not be telegraphed) to meet Bruce, Bruce told Ed to
"make a move."  He didn't say throw a punch or throw a kick.  He just said
"make a move."  Ed's hands were up and Bruce's were at his side.  Ed asked
Bruce if he shouldn't put his hands up as well, and Bruce replied, "I'm
ready!"  Ed threw a left jab, and next thing you know, Ed's arms were
trapped.  Ed's going, "Damn, what happened."  So, he walked around a
little, and I was chuckling.  Ed came back and said, "Hey, let's try that
again," and the same thing happened!  That's what happened to everybody who
came, and there were some pretty tough and rough guys.  All had boxing or
other fighting backgrounds.  Bruce would say, "Make a move," and he would
shut us all down; he could do that.  No one I've ever seen could shut you
down like Bruce did!  Like I said, I've never seen anybody like that!