I agree with Eduard completely. Very nice post, sir!
DVD burners (the physical drive) are a dime a dozen these days. Even high quality ones are inexpensive, and there are a number of software solutions out there to simplify the burning process. As was already mentioned, Nero is probably the best. Roxio is a popular alternative. If you were to research "Top 10" lists of DVD burning programs, these would usually be #1 and #2 respectively.
External hard drives are also relatively inexpensive these days. You can get a good 1TB drive for about $70, and if you're lucky and spot a good sale, you can get a 2TB drive for about the same price. Seagate and Western Digital are the two best brands. LaCie makes a superior product, but their prices are significantly higher.
DVD vs HD
There really aren't any advantages of DVDs as storage anymore. They are more of a transfer solution than a permanent one, meaning if you want to give copies of your photos to someone else, burn a disc for them. I would argue that low capacity flash drives are a more viable option for transfer, but it's easier (and usually cheaper) to buy 100 DVDs than 100 flash drives.
DVDs are a good backup to the backup, if you have no other means. As Eduard said, redundancy is the key. However, with today's technology, it's better to go virtual and have your stuff stored in a cloud that is online and offsite. In case none of this makes sense and is only adding to the confusion, here's the short and sweet:
#1 Backup to an external hard drive. Fast, easy, automatic, and comes with software.
#2 Backup online. Easy to set up, automatic, off-site, and has annual or monthly fees.
#3 Backup to DVD. Slow, tedious, hands-on, and requires purchasing software and disks.