So... solution one is to make sure your backups are automated... They don't require someone to remember to change a tape or cartridge etc...
Solution 2... make sure that if the backup fails then someone is notified and they actually do something about it... Do you have a system in place to check this and make sure it happens. Is the backup status of your critical servers reported to the directors during management meetings?
Solution 3... backup off site. Be this online backup which we prefer especially with the cost of this being really affordable these days or taking tapes or USB drives offsite. If your site become inaccessible then you need a plan B... With our online backup facility, you can access your data on a remote server so get up and running a lot quicker than traditional offsite backup. Ask us for more info rather than me boring you with the detail now...
Solution 4... multiple backups... So traditionally we tend to run a windows server backup, i.e. using the software that comes with windows server (used to be called ntbackup). Then we run an online backup if the client agrees to the investment and finally like to sync the main data to an external USB drive. These are all pretty much low cost ways to backup but are worth their weight in gold.
Solution 5.... Now we start getting to the nitty gritty.... If your server fails then you need to get it backup and running as quickly as possible. This is where third party products come into it. The traditional third party products backup your servers data up, especially exchange and sql server and make it easier to restore the data. Reporting and configuration and options all tend to be a lot easier using third party products but can be really expensive. Where the real value lies is in snapshots... If you use backup software to take an image of the server then restoring an entire server can be as quick as an hour. We have used Acronis in the past on a number of servers and it does the job for us.
Actually to be fair, windows 2008 includes this facility which recently saved our bacon. So the moral of the story is, it doesn't have to be that expensive to setup backups that will prove to be quite simply priceless when they are required.
Hope this post helps, no doubt others have a lot of different experiences and advise but the above information is from our 14 odd years of practical experience so i hope it proves of some use.