You can try the following:
If you have OpenJDK Java 7 Runtime installed in your system, then you should have a file named openjdk-7-java.desktop in the folder /usr/share/applications/
Check if you have the .desktop file.
Go to the terminal and type:
cd /usr/share/applications
ls -l openjdk-7-java.desktop
If the result is:
-rw-r--r-- 1 root root 367 Oct 24 22:29 openjdk-7-java.desktop
Then (to associate OpenJDK Java 7 Runtime to the java files) you can edit the file defaults.list also in the folder /usr/share/applications/ .
In the terminal type:
sudo gedit /usr/share/applications/defaults.list
Search for application/x-jar and application/x-java-archive in the defualts.list, and change the .desktop file to the openjdk-7-java.desktop and save the changes.

Now the java files should be open with Open JDK 7 by default. To double-click and run, make sure the file has execute permissions.
You can set the permissions in the terminal with: chmod 755 file.jar
or right click in the file, permissions tab and click in "Allow executing file as a program"

Finally double-click in the file to run it.
Hope this will helpful!
Regards.
Best Answer
GUI
Depending on which Ubuntu version you have,
Before 13.04
In Nautilus, go to this menu:
13.04 and later
In Nautilus, go to this menu:
Then,
in the 'Behaviour' tab, enable "Run executable text files with they are opened"
Command line
If you prefer a command:
Note: Both GUI and command line methods work only for Nautilus (the default graphical file manager in Ubuntu)