The ESV Bible is currently available at Amazon as a Kindle download for free.
I know I’ve got ESV in other formats, but this is free.
I know I don’t have a Kindle or a iPad (which can run Kindle as an app) yet, but when I do I’ll have a library ready to go, thanks to Kindle app for iPhone.
(If you get there and it’s not free anymore, you know the offer has ended.)
HT: Nathan Bingham.
mgpcpastor's blog 
You can always get it free as a pdf (just google i forgot the site) and then convert to the kindle format.
I wasn’t able to identify a link for this.
I’d only post a link that was recognised by the ESV’s publisher.