There are currently a few different services that can provide unlimited ebooks to your device with a subscription. Here is some information:

Kindle Unlimited: This is the only real option for those of you that have e-ink kindle device. (it doesn’t allow for any apps – so you can only use this service)

Price: $9.99 per month
Content Available: around 600,000 ebooks and audiobooks
Compatibility: iOS, Kindles, Android, Windows and Blackberry
Free Trial: 30 days

Scribd: 

Price: $8.99 per month
Content Available: around 500,00 ebooks, 45,000 audiobooks, 10,000 comics and documents (including sheet music, scientific studies, and court cases)
Compatibility: iOS, Android and Kindle Fire (not e-ink)
Free Trial: 14 days

Oyster:

Price: $9.95 per month
Content Available: 1,000,000 ebooks
Compatibility: iOS, Android, Kindle Fire (not e-ink), Nook HD and web
Free Trial: 14 days

Overdrive:

Price: Free (one just needs a library card)
Content Available: depends on your library’s membership – ebooks, audiobooks, periodicals, video
Compatibility: iOS, Android, Windows 8 phones and tablets