As your chain gets older, it will stretch out. What you can do is measure12 links with a tape measure. For a brand new chain 12 links should be exactly 12 inches long. If you ask around, most people will tell you to replace the chain when 12 links measure at 12 and 1/16 inches (ie enough of the chain wears away so that it is now 1/th of an inch longer for every 12 links).

If you are going to replace the chain, be sure to look at the condition of your chain rings (the rings on your cranks) and also the cogset to see if they are worn badly. If your chainrings and cogs are worn out and you put a new chain on your bike, that chain won't last long. The chainrings and cogs will wear with the chain, so you might have to replace everything depemnding on the condition they are in.

As for dirt, the type of chain lube you use can affect how dirty the chain gets. I use White Lightening lube, which is a dry lube. It goes on wet, but the liquid evaporates away, leaving a wax-like lubricant behind. The advantage of this is that dirt does not stick to a dry lube like it will a wet lube, so the chain stays cleaner. However, if you often ride in wet, rainy conditions, you may want to stick with a traditional wet lube.

I think Triguy98 said it best though: Clean your chain more often, and it won't be so bad.

If you are unsure of how to properly clean and lube your chain, ask your local bike shop to show you how to do it properly.

not quite, BrianMc... you should change your chain starting from 2000km ridden... then the chain won't mess the cassette...

Yeah, I have been told the same thing. The cassette stretches the chain but also wears down, so changing only one component leads to parts that don't quite mesh well enough together.