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Updated
SpecsUpdate
Pros
Pro Beginner-friendly
DigitalOcean has a control panel that's intuitive and easy to use, new servers (Droplets) can be spun up in under a minute and they offer stock "apps" (LAMP, RoR, Wordpress) that can be deployed instantly. There's also an extensive documentation for people new to VPS.
Pro Good API
DigitalOcean has an API for creating and destroying droplets and replicating droplet control panel functionality. The API is RESTful, uses oAuth, supports IPv6 and comes with an extensive documentation.
Pro Great customer support
Quick and knowledgeable customer service, extensive documentation and helpful community.
Cons
Con Don't accept Bitcoin yet
Even though it's one of the most voted suggestions on their customer feedback website, DigitalOcean does not accept any crypto-currency payment methods.
Recommendations
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Flagged Pros + Cons
Pro Free credit for referred users available
If you use a referral link to sign up you'll get $10 credit. Additionally if you sign up to the newsletter you can get another $10 credit, which is also available for existing users.