var directory should be readable and writable by web server. If you know the user and group of the webserver it is recommended to use a different set of permissions:
# chown -R user.usergroup var/ # chmod -R 770 var/
If not then # chmod -R 777 var/
Try clear the image aliases cache and view cache from admin interface. If you use ImageMagick, make sure that path to convert script is correct in the settings/override/site.ini.append.php
Do you have any errors in the var/log/error.log or in debug output?