Amazon just posted an Official Announcement that Kindle book lending is now available. Detailed instructions are on the Kindle Help pages and the recipient does not have to own a Kindle (but does need email and access to the web (on a device that lets the Kindle for Web app run) or a device with a Kindle app. In general, the terms are the same as the heralded lending on the nook:
Eligible Kindle books can be loaned once for a period of 14 days. The borrower does not need to own a Kindle -- Kindle books can also be read using our free Kindle reading applications for PC, Mac, iPad, iPhone, BlackBerry, and Android devices. Not all books are lendable -- it is up to the publisher or rights holder to determine which titles are eligible for lending. The lender will not be able to read the book during the loan period.
I just checked thru my own library (the Manage My Kindle page is where you set up the loan) and most of the ones I've picked up lately are apparently non-loanable (shock! the same publishers that raised prices also don't like lending!). Out of the first page of titles, only five are lendable (and all but one were free books).