I don't know the largest, but definitely it can handle large systems. A recent website I deployed (afrigatenews.net) is getting around 400K hits / month
I have also other 3 website ranging from 50k - 500k+ hits a month.
I highly recommend the SSD power especially for mysql and redis performance. I just wish they will allow separate disk scaling and add a bit more CPU power.
I feel the SSD power is the least captivating feature of them. Just 20 GB of SSD power isn't enough for most production uses. Their main selling point is that they're cheap and you can spend just $5 for a decent server that does tasks like crawling, sending the data to another server that stores it.
From the recent article related to DO's $37.2M funding 
“Flywheel built an entire WordPress hosting service on top of our cloud,” Uretsky said. “They are running over a thousand droplets for their users. The integration is so tight that customers can’t tell that we’re running the service.”
Another example, Beyoncé launched her new album in December. It turns out that Beyonce.com runs on DigitalOcean. The servers handled the album launch without breaking a sweat.
“We’ve seen 15 million visitors within the first 24 hours. She’s been pretty happy with the service,” Uretsky said.
Re SSD disks, as someone who's using both Digital Ocean and Ramnode: For PostgreSQL on smallish data sets (5GB) doing Sphinx reindexes every few minutes Digital Ocean's I/O performance is much lower than Ramnode's KVM SSD instances. Disk benchmarks on the two gave me 5-10x in Ramnode's favor on small instances. Digital Ocean is still pretty decent for a budget provider and Ramnode has all the standard issues of a smaller hoster (and all the advantages), but if I/O performance is critical to you it might be worth taking into account. DO is much slicker, though.