The Origins of OOP
OOP is the most popular of the big three programming paradigms.
So who invented OOP?
Well, it's difficult....
The terms "object" and "oriented" in the context of object-oriented programming were first used at MIT in the late 50s and early 60s.
There seems to be some conflicting information on the internet on who invented object-oriented programming.
The earliest example of object-oriented programming was Sketchpad which was a program written by Ivan Sutherland in 1963.
On a side note, you should have a look at the demo of Sketchpad, it's stunning how ahead of it's time this program truly was.
The first object-oriented programming languages (Simula I and SIMULA-67) were developed by Kirsten Nygaard and Ole-Johan Dahl in the 1960s.
It is noteworthy that Simula was not inspired by Sketchpad in any way, the development of Simula happened independently of Sketchpad.
Simula 67, which was released in 1967, had many features we are used to in modern object-oriented programming languages like objects, classes, inheritance, subclasses and so on.
I found some sample code on Wikipedia  which demonstrates how modern Simula looks:
Begin Class Glyph; Virtual: Procedure print Is Procedure print;; Begin End; Glyph Class Char (c); Character c; Begin Procedure print; OutChar(c); End; Glyph Class Line (elements); Ref (Glyph) Array elements; Begin Procedure print; Begin Integer i; For i:= 1 Step 1 Until UpperBound (elements, 1) Do elements (i).print; OutImage; End; End; Ref (Glyph) rg; Ref (Glyph) Array rgs (1 : 4); ! Main program; rgs (1):- New Char ('A'); rgs (2):- New Char ('b'); rgs (3):- New Char ('b'); rgs (4):- New Char ('a'); rg:- New Line (rgs); rg.print; End;
The reason Simula 67 looks so modern even more than 50 years after its creation is the simple fact that Simula 67 heavily influenced Java and C++, among the most popular OO languages to date.
The definition of OOP
In 1967, influenced by, among others, Sketchpad and Simula Alan Kay coined the term "Object-Oriented Programming". 
I wrote my first program that I would call object-oriented in 1962. And people have been writing programs in that style even earlier than that. -- Alan Kay 
The definition of OOP that most programmers would come up with today is very different from the definition of OOP by Alan Kay - the term got "colonized" to what it is today. 
OOP to me means only messaging, local retention and protection and hiding of state-process, and extreme late-binding of all things. It can be done in Smalltalk and in LISP. There are possibly other systems in which this is possible, but I'm not aware of them. -- Alan Kay 
Since the definition of OOP by Alan Kay differs from the understanding we have of it today, it's sometimes referred to as "Message Oriented Programming" so as not to get the two confused.
If you want more in-depth information about "Message Oriented Programming" here is the best explanation of it I could find.
Smalltalk which was created during the 70s is the third object-oriented programming language. It was created at Xerox PARC by a team led by Alan Kay.
Smalltalk was not only a programming language but also a live dynamic development environment where you can debug your program while it's running. It's very different from what programmers are used to nowadays.
Here is a great talk that shows this environment and the workflow one would use when working with Smalltalk.
The first public release was Smalltalk-80 and had a respectable market share during the 1980s to mid-1990s before getting killed off by Java.
Smalltalk was very influential and influenced almost all object-oriented programming languages that followed it.
 Alan Key's answer on Quora
 Seminar with Alan Kay on Object Oriented Programming (VPRI 0246)
 What is Alan Kay's definition of Object Oriented? Alan Kay's answer on Quora Alan Kay email exchange