If you have an Acoustic Guitar:

Here are a couple of questions to answer:

1) Have you had the same strings on for over 2 months?
2) Are your strings rusty?
3) Are your strings rough?
4) Do your strings sound dull?
5) Had a string break recently?

If you answered yes to any of the above, its probably time to replace your guitar strings.

Because of moisture on your fingers and in the atmosphere, strings corrode and rust over time and their ability to vibrate diminishes. This not only causes the sound to dull but even worse, the feel of the strings becomes rough and will hurt or even damage your fingers.

Strings can also become brittle from too much vibration, just think of how a paper clip snaps if you twist it too much, the same happens to strings.

If you play a lot, say for 2 hours a day every day, then you should look at changing your guitar strings every month.
If you play less, but still strum most days, the max you should leave them on the guitar would be 2 months.

Strings are quite cheap, about £5 for a set of 6.

There is an alternative to changing your strings this often. You can buy coated strings. These last longer due to a coating on the strings that prevent dirt build up and corrosion. Coated guitar strings tend to last 3 to 5 times longer than normal strings, so you can leave them on for longer. These still need to be changed though. At least every 6 months these should be changed as they are also prone to breaking because of the vibrations of the string as explained earlier using the paper clip analogy.
Coated strings do cost more, about £12 for a set of 6, but last longer, so can work out more cost effective.