CD DVD Burners

What they do
They allow you to write on CD or DVD.
 
Quality to consider before purchasing one
You should consider several factors: reading quality, writing quality and reliability over time (besides speed of writing, although this is less important given that nowdays different makes have a similar speed).

 The reading quality is important when you have to read CD (or slightly damaged DVDs), or recent games with the most recent types of protection. If your device is not great at reading, you may be unable to play some of the most recent games (or some of them may make a terrible noise before starting) or disks containing even a slight error may cause you problems.

The writing quality is very important to write CDs and DVDs which can last. Besides making a backup of your original games (which is very easy with good CD/DVD writers), high quality CD and DVD burners (e.g. Yamaha, Plextor for CD and Pioneer for DVD), are excellent at writing even stuff that come from lower quality products, and these CD and DVDs will work perfectly for several years. For DVDs the situation is even more critical given that you may end up having to throw away lots of them before you are happy with the quality achieved. Furthermore, even if you reach a quality you are satisfied with, the DVD may not work after a few months.

It is also important to remember that writing faster does not mean writing more accurately or better; the greater the speed, the greater the chance to lose some data in the future (for this reason I would advise you to choose an average burning speed).
 

The cost for CD burners is between 30 and 100 USD, and for DVD burners (which can also write CDs) is between 40 and 120 USD .
Brands to keep in mind (CD DVD Burners sale)

For CD burners I would suggest the following:
(I haven't suggested Yamaha, currently out of production, which would be just as good as Plextor)

1) Plextor
2) Teac
3) Ricoh

For DVD burners, I would suggest the following:
1) Pioneer (by far the best ones)
2) Plextor
3) Sony
4) Panasonic

Other interesting makes are the following:

5) LG (although not recommended if you have to write lots of DVDs)