Deleting Windows forever, dual-booting Ubuntu and Slackware.
 

My only question is Windows is the primary partition, and Ubuntu is not. How do I remove Windows to make Ubuntu the primary one and Slackware the logical?

Thanks

EDIT: as long as I don't install LILO and run sudo update-grub, there shouldn't be any problem booting Slackware, right?

What are planning to do ?
Move UBUNTU to the primary partition ?
Or reinstall UBUNTU ?
Moving UBUNTU without reinstalling UBUNTU means the you have to change the UUID in the menu.lst or GRUB,cfg depending with version of UBUNTU you're using
Removing windows that is not the problem
Why not Slackware in the primary partition instead of windows and installing LILO on sda1 instead of MBR.
If it is anyhow possible to do so with LILO.