There are a couple of reasons why thumbs don't show up. At first you have to check if the thumbs are visible in the back end. Of so you it's most likely an issue which occurs in your browser since the server can render images. The following lists point you so some of the most common issues.
mod_secure: Please ask your provider about possible issues with that. Doing this solved 99% of the issue.
Error 500: PHP memory size too low. I have good experience with 128M. Depends on the size of your images
Error 500: weak server. Every thumbnail request is a PHP request. Some servers can't handle the necessary amount of parallel PHP requests.
Error 500: the PHP function
imageconvolution does not work on your server. For now one user reported this using PHP 5.3.8. After commenting out the line of code the gallery worked fine.
Do not use special characters in your file names like Umlaute, +, or things like this. Make your file names safe for the web.
Install GD library for image processing
Issues with image sharping. Try to disable it using the components configuration dialog.
PHP should have write permission to
Picasa Images do not show up because the method
get_file_content is not working. Check with your hosting provider to solve this issue.
allow_url_fopen should be enabled.
Error 500: PHP should be able to execute the script
/components/com_eventgallery/helpers/image.php in order to display thumbs.
Try to use Use Rendering Fallback and contact your provider if this works for you so he can change the server settings.
Log file is too large: delete
Sh404SEF: you might want to configure the Flooding Protection to prevent images from randomly disappearing.
The PHP method
fpassthru is disabled. This method is necessary to deliver images from the server to the browser.