I am facing an aquifer at every conceivable location it seems. I finally figured out how to tunnel through on a freezing map, but I don't want to spend so much time above ground. My dwarves need their tunnels.
The Lazy Newb Pack way: Just click the Aquifers button after running lazy newb pack.exe
Changing WorldGen Settings: Courtesy of Chrissi from the bay 12 forums
To actually answer the question.... yes, you can render a world with significantly less aquifers (I have done it) by increasing the minimum elevation in the parameters. Try 20 or 40 or something. It also reduces oceans, but oceans are what cause aquifers in the first place.
Obviously this has other side effects on world gen like making the world more mountainous and making oceans smaller/nonexistent depending on how high the minimum elevation is. There is no option to just turn off Aquifers in the advanced mapgen, although I believe some mods do have that option.
Text editor (All operating systems) Find the files in Dwarf Fortress/raw/objects (new world) or Dwarf Fortress/data/save/regionNN/raw/objects (already saved world). Open the three files with a text editor (e.g. Notepad). (inorganic_stone_layer.txt, inorganic_stone_mineral.txt, and inorganic_stone_soil.txt) Use Edit->Replace, and replace [AQUIFER] with (AQUIFER). (Use 'Replace All'). To restore the tags later, do the same in reverse. (Replacing (AQUIFER) with [AQUIFER]).