Whether you're backing up your Mac with Time Machine or another service, it can be an incredibly time-consuming process. Over at How-To Geek, they walk through a number of the folders you can probably skip if you need to get that backup done quickly.
By default, a service like Time Machine doesn't include system level files or your Trash, but there's a lot of other potentially useless stuff you can get rid of. If you pop into the Option panel for Time Machine, you can exclude files and folders from your backups. How-To Geek points to some obvious stuff you can exclude here, like your Dropbox, Google Drive, or iCloud folders.
Other files to exclude can include your virtual machines, Steam library (awkwardly stored under
~/Library/Application Support/Steam), and your downloads folder. You can also usually skip large applications like Office or Creative Suite, because they're not only easy to download again, they're also usually tied up to system level licenses, so they're not always easy to transfer over to a new computer anyway.
How-To Geek also shows off an extreme approach, which happens to be the one I personally take, which excludes all your system files and all your applications. This means only important documents get backed up, which keeps back ups small and fast.
This means you'd need to completely reinstall the OS if a hard drive fails and download everything again, but considering the Mac App Store makes that pretty easy to do, it's a solid approach if you just want lightweight backups. Head over to How-To Geek for more info on how to tweak your Time Machine backups.