Is there a Portable MySQL
Yes you can have MySQL as independent ZIP archive and it is also available for download in MySQL download page for windows, do the following steps 


Download ZIP archive
Extract/UN-zip the archive
Change the default ini file if needed
You may also install service or start mysqld from cmd prompt using 

cd \bin
  mysqld.exe  


or if service is needed to be installed

cd \bin
   mysqld.exe --install MySQL Service Name --defaults-file=Absolute Path to .ini file


use mysql.exe -uroot to login MySQL


The ZIP archive is also available for UNIX* OS

Hope it helps