To find the articles/chapters/pamphlets you can actually download and read, you can limit your search to content you can access. Go to the Advanced Search page and find "Select an access type." You'll see the following options:
All Content: All the things on JSTOR.
Read and download: Content you can download or read online. This will include Early Journal Content and journals/books publishers have set to free.
Read Online Only: Things that you can only read online (this is for people who have a MyJSTOR account and participate in Register and Read).
Purchasable content: Content you can buy.
JPASS subscription content: Content you can read and download if you have a JPASS.
Just pick an option after you've developed your search and find the stuff more relevant to your needs. You can also narrow your search results after you've done an initial search. You can find that option beneath the 'access level' checkbox, at the bottom on the left hand side of the page.
Now, you need never know the frustration of finding a great article and being unable to read it. Woohoo.