The sun is running out of Helium in it's core. In about a billion years, it'll be hot enough that all our oceans will boil. On it's way there, this will cause greater evaporation, and may in fact increase rainfall for a time, but by the time the oceans are boiling, atmospheric water will be hot enough that it splits back into to hydrogen and oxgen molecules, which will let them escape the atmosphere. Exactly how quickly this will happen, nobody knows, and physicists like to argue about it, but nevertheless, it's a safe bet that during this time, it will eventually stop raining - because there will be no water left on earth to rain with.
On the downside, we may get some interesting replacements for rain, as things with higher boiling points start to evaporate instead. If it is still raining at this point, you definitely shouldn't go out without an umbrella.