Two scientists at the Harvard’s Wyss Institute have successfully stored a 700TB of data in DNA.
To give you an idea of how big this is, it would mean more than 35000 years of HD video of YouTube (720p at 5kbps) into a single gram. HD video is indeed a diffcult thing to store, it is even mentionned in the video. This means it is almost 60000 times more dense than a 3TB hard drive and it should fail a lot less often.
While they were able to generate that amount of data, most of it was duplicated. DNA replication is really fast, encoding the data is however much slower. They don't extrapolate on the read time either. It is not tomorrow that we will have DNA USB keys, but for long-lasting and space-hungry data, it is very promising.
A rather long time ago, tape devices held a similar function. It is now pretty obsolete, but it made the first backups possible.