Laravel works fine local, but on the server I get the following:
Laravel requires the Mcrypt PHP extension.
However I can't install mcrypt on my server because i have no admin rights. The process for installing the module at the server in my corporation would be to painful, it would be better to just go with another framework instead. But Laravel seems so modern and beautiful that I can't let it go without asking this question: Is it somehow possible to run Laravel without php-mcrypt?
No, Laravel really requires the MCrypt Extension. You could, however, ask your hosting provider to install the MCrypt extension.
If you decide not to use Laravel, instead take a look at Symfony. Symfony is another very powerful framework and Laravel makes use of quite some of Symfony's features.
Link: http://symfony.com/
Symfony doesn't require this plugin to be installed, however it requires the following plugins (but I assume those are installed at every hosting provider):
I hope I helped you further :)
EDIT: Newer versions of Laravel don't need to have Mcrypt!