A typical claim that you can see from creationists will look like this:
“Up until the recent past, when the top of Niagara Falls was reinforced with concrete, the water was carving a channel upriver toward Lake Erie at the rate of about four to five feet per year. Since the cannel is now about seven miles long (35,000 feet), this means that the age of Niagara Falls is between 7,000 and 8,750 years old (or less). This, of course, assumes that the rate of erosion has been constant.”
You can replace “Niagara Falls” with “Mississippi Delta”, “Sahara Desert” and/or various and sundry other geological features and get a very similar claim.
The problem with this claim should be pretty obvious: there is no requirement that Niagara Falls be the same age as the entire Earth!
Currently Niagara Falls is cutting through sandstone at the quoted rate of 4-5 feet per year. If you look further upstream, you see that Niagara Falls previously cut through other types of rock which erode more slowly than sandstone.
The real age of Niagara Falls, using reasonable erosion figures for those different types of rocks, aligns with the last Ice Age. The Falls were formed by glaciers a very long time after the Earth was formed. There is no mystery here.
So while the age of Niagara Falls establishes a minimum age for the Earth – it could hardly be younger than the Earth itself - it implies nothing about a maximum age for the entire Earth.
This same response is valid for the Mississippi Delta, or any other local geological feature on the surface of the Earth. The surface of the Earth is constantly changing. To point to any single local geological feature and say that its age must equal the age of the entire Earth is simply absurd.
 http://www.earthage.org/youngearthev/evidence_for_a_young_earth.htm#Niagara%20Falls:, referenced on June 19, 2008