First, they serve as good sources for quotations about how awesome you are. You can take phrases from them and put them on a references page on your website.
I used a photo of some notes on the same page on my site as a reminder that yes, the letters really are real, I didn't make them up.
Some people will put an image of a cake on their site with superimposed quotations from the thank you notes. That's a good way to show the cake that they're thanking you for, and to make the connection between the product and the praise.
If you want to be more direct, you could write to the people who send you a thank you and ask them if they would give you an online reference, with a link to whatever site you like to use. If a client is willing to write you a note than they'd probably be willing to write a reference as well.
You can also post excerpts from thank yous on facebook or other social media sites. That will show that you do actually have a client base and that they like your product!
Finally, you can make up a reference sheet for cases where people ask for a reference. A lot of the time people will write that they'd be glad to be a reference for you, and if you keep track of that it will make giving out references much easier.
Do you have any ways that you use thank yous that I didn't mention? Add your suggestions in the comments section below.