[EDIT] The last version of MAMP with the last version of OSX Yosemite works fine.
I installed the beta of Yosemite two month ago, no problem with MAMP. With the last
I have resolved the situation by changing the default Port of Apache 2.4 updated after upgrading to MAC OS Yosemite.
The file is located in: /etc/apache2/httpd.conf
Change Listen 80 to Listen 8080
Restart your MAC, and try to launch again MAMP Services.