Your reaction to the drive space problem depends on the type of environment you're talking about.
If this is a production database that feeds a live website for a business and your data, log and backup files live on a SAN, then have the SAN administrator allocate more space to the volumes. You may get into the game of who pays for it, but you have a clear path forward. After the crisis is addressed, set up a longer-term solution to monitor your space. After you collect some history, you can use it to forecast when you'll run out of space and let your SAN administrator know before it becomes an emergency. There's an article on this at http://www.sqlservercentral.com/articles/Drive+space/134523/.
If this is a home lab used for development and play and you're on local drives, then take whatever approach you want because you don't have to worry about keeping production up and running. Buy a different drive, move some (or all) of your database files to it and run them from the new drive. Then you'll have the old drive for whatever you want.
Whatever you do, you have to stay within the constraints of your physical media. If you don't have any files on there that can be deleted or moved and you don't have any way of adding space to the drive, then you're in a tough spot. I'd say you've outgrown the hardware you have and it's time to either add some, upgrade what you have or get new hardware that's appropriately sized to the anticipated growth over the life of the server.