I guess a .jar file is very capable to run in most OSes, since Java Virtual Machine is pretty much available & installed in many computers anyways!
An .exe file just works in Windows (and sometimes in WiNE)!

 I agree with your answer but :
with processing it's not the case. the "Export Application" produces more than one file. And the sketchName.jar file is not alone , there are other jar files , for example the libraries.jar files.
How do we do with these files to have only one .exe file ?

When exporting a sketch (CTRL+E), Processing generates various kinds of files.

However, for an offline experience, you only need the .jar file.
And if your program uses external files like image, sounds, etc.; you have to include the /data folder as well!

when i use File/"Export Application" I have :

in the error file i have:

there is an issue with the main class:
where must we put the main class and what must contain this class ,

the lib file contains :

It's not so simple to make with these datas an alone .exe file
Help me if you have explanations.
Thanks for your detailed contribution

Well, I still use v1.5.1. And it seems like things got a lil' more complicated in current beta versions!

When I press CTRL+E, Processing v1.5.1 creates a folder called /applet.

Within it, there are at least 5 files:

• index.html
• loading.gif
• .pde
• .java
• .jar

Perhaps you can use softwares like Launch4j (used by Processing itself) to package all these files into one.