This is a list of sites that are extremely helpful for finding the great fonts to use for web design and for graphic design. Many of these sites will let you generate free text samples, which you can use in your mockups to sell the client on the font and get purchase approval.
My Font
http://www.myfonts.com
My Font offers a huge selection of premium forts for web, typography and graphic design. The great feature at My Font is the ability to generate text samples of their huge seleciton of premium fonts.
AWWWARDS
http://www.awwwards.com/100-greatest-free-fonts-collection.html
The AWWWARDS puts together amazing collections of the years best web fonts. This list is a must read for all designers and is very helpful for beginner designers who are looking to accelerate the development of their style.
Lost Type Co.
http://losttype.com/
This typography co-op allows users to donate what they wish to use this beautiful collection of fonts designed by Tyler Galpin and Riley Cran.
The League for Movable Type
http://www.theleagueofmoveabletype.com/
Offers a professionally curated selection of open-source typography.
Font Squirrel
http://www.fontsquirrel.com/
Font Squirrel has a great collection of free web fonts and most importantly a web font generator.
Google Webfonts
http://www.google.com/fonts/
A nice selection of open-source web fonts offered by Google that are very easy to integrate into your website.