I work in IT and have the joy of dealing with backups and redundancy, in terms of the redundancy in particular over the years it is absolutely incredible how many 'failproof' solutions I have witnessed that have in testing during implementation worked great, but of course as soon as there was an actual issue that required failover they don't work!
Backups are important but even more important is then testing you can actually read them and retrieve data from them! What I really really hate though is when a user gets in touch saying they've lost a file...from 3 months ago as tape backups might be an air tight solution but they're not exactly the fastest things in the world to restore from!
I worked in IT for around 15 years between two companies. One project that caused a big problem was when a new phone system was installed and being a financial sector company, all calls had to be recorded. The recommended device saved the calls as wav files to DVD's... I raised the question of how to back up these disks as under some obscure data protection law data had to be stored for six years, and at the time most DVD manufactures could not guarantee that the dye structure would be retained so the disk would need storing in enclosures in a controlled environment to avoid degradation. What they also go wrong was the estimated number of DVDs we would need for storage. We were changing DVD's upto three times a day on some occasions... On one occasion I was tasked with retrieving the recordings of a call that happened 9 months before... this had to be a manual process and was a real pain and the more times disk were removed and handled the higher the risk of damage... DVDs were certainly not the ideal way to store this data.
The last company we used shadow copy to mirror the live servers so in the event the live developed a fault the users simply logged out and then logged back in for the change to be picked up... it worked in practice which was quite amazing. Off site backups were high density tapes... and I can sympathise with you when you need to restore an old file from an old backup tape.... we used two drives, partly for redundancy, but mainly due to the daily, weekly and monthly tape structures we used. The daily backups consisted of five tapes, one for each day. Four weekly tapes 1-4 and six monthly tapes 1-6. Each daily back up was mirrored to the weekly tape which remained in the drive each night. The daily tapes were changed each morning, and the previous days backup taken off site. On Monday mornings the weekly tapes were changed and the previous weeks tape taken off site. On the last working day of the month the weekly tape was substituted for a monthly and the weekly tape taken off site.... sounds complicated, but it worked.
One thing the company did consider as part of a disaster recovery plan was having a complete skeleton set up in another office they owned so in the event the building was evacuated business could continue to a degree. I then pointed out that this building was fed off the same substation and in the event the reason for moving was external power issues then it wouldn't work !