Unlike the first SMB, in SMB3 at the end of each world you fight one of Bowser's Kids.
Each with their own unique style.
Of course you fight Bowser on the last level of the last world!

Larry Koopa
    
A good Koopa to start with. Fairly easy. A nice warm up.

Morton Koopa Jr.
    
Morton is waiting at the end of World 2, he ups the challenge from Larry a little bit.

Wendy O Koopa
    
Bowser's daughter defends World 3.
She will throw circles at you. . . .yes, circles. (Or hula hoops perhaps)
They actually do pose a decent threat.

Iggy Koopa
    
Iggy awaits you at the end of World 4.
He's. . .not very challenging.

Roy Koopa
    
Now this Koopa has power!
When he lands from jumping he freezes Mario (if Mario is touching the ground).
Very similar to Sledge Bros.You gotta be consistently jumping in this battle

Lemmy Koopa
    
This kid has a ball.
Not only does he ride on a ball,he throws them at you, which bounce all around!
One of the hardest Koopa Kids, if not the most.

Ludwig Von Koopa
    
The last Koopa Kid you battle.
He is said to be Bowser's Second in Command.
He brings a decent challenge.

King Koopa/Bowser
    
Bowser's back!
After battling him for the first time in Super Mario Bros, fans were wanting to see how he would look and fight in SMB3, especially since he was noticeably absent from the second SMB that North America received.
He entered SMB3 looking bigger and more fierce.
Unlike his kids, jumping on Bowser harms you! You must defeat him another way.