can download easily — there all free fonts for web and desktop use. Actually Google Fonts are no links to download the files, but all Googly fonts you can find and download Fontsquirrel.
Typekit on most fonts paid and to download them you will not be allowed: need to buy a license for Adobe Creative Cloud or pay a subscription to Typekit itself.
But typetoken fonts there are pitfalls with licensing. They can be inexpensive when using the computer, but be costly when you use on the website. About them I have a blog article paulradzkov.com/2014/web-fonts_license
If you are a designer, it is important to remember that.