So I've been given a lot of patches from all kinds of companies like Stride Animal Health, Rock&Roll denim, etc. etc. 

My question is... what do I do with them? Is it appropriate to put them on my show shirts without me being sponsored by them? Like isn't that the intention? Or is there an unsaid rule that you can't put patches on your shirt unless you are sponsored by that company???

Personally I wouldn't put them on my shirts without them giving me a sponsorship.  If they want you to advertise for them then they should fork out the money.  Plus I miss the good ol' days of all the pretty shirts, Now the shirts look like walking billboards

I agree with Euchee. I wear one patch that is from a company that I am sponsored by and use most of their products. I only have good things to say about that company and their products.  I have received patches from other companies and they go in the trash as it is no benefit to me to wear it and give them free advertising. I also think that if you are wearing a patch, you should be fully informed about the company incase someone asks a question. If I am not sponsored them, I am typically only informed on the products I use.