Copper: You've probably already seen me use a lot of copper wire in projects on this site because I use this for my practice wire. However, it also looks nice with some designs that use earth tone colors. Copper will darken and discolor with age, which is called a patina affect. If you prefer to keep your copper wire bright, you can simply polish it. I've also sometimes soaked copper in white vinegar to clean I up a little.
Galvanized: You can find this (along with copper wire) in most hardware stores. It is a dull silver color and is also good practice wire. This wire is harder than the silver wire you may be used to, so get a small gauge if you plan to get some.
Sterling Silver: This is one of my favorite types of wire because sterling wire works the best for many of my finished jewelry pieces. Sterling indicates that the wire is 92.5% pure silver. The rest is made up of alloys (such as copper or zinc) to provide strength. Sterling will tarnish, called oxidation, so it's best to keep in zip lock bags or sealed containers of some kind when not using it for jewelry or wearing the jewelry itself. When it does tarnish (and it eventually will), you can polish by using a polishing kit, using a magnetic polisher or tumbler, or you can clean it with an ionic cleaner.
Fine Silver: Made of 99.9% pure silver, many wire workers enjoy working with fine silver. Fine silver is softer than sterling. Since it has fewer alloys, it also does not tarnish as quickly as sterling silver does.
Gold-filled: First of all, never call gold-filled wire, "gold wire." I've seen this too many times from jewelry makers, whom I hope, just don't know any better. While gold-filed metal has many layers of gold, it is not pure gold. On the upside, gold-filled is of much better quality than plated gold (only one layer) so gold-filled lasts for a very long time if cared for properly. It is a wonderful alternative to gold, which as you can image is pretty darn expensive!
Gold: If you are daring enough and feel comfortable enough, go for the gold! Many jewelry vendors offer real gold wire in various karats (10-24 for example) and even different colors.
Coated Colors: Often coated wire is coated with an enamel to create the color of the wire. This wire has become very popular and is even available in many large craft stores. It is a lot of fun to work with. However, due to the coating, it can be marked by metal tools, so keep this in mind when using it.