Hmmmm.. I've only done minimal work with magnetic fields during the past few years.. But, from my observations, I believe that Artofkicking may be correct.
If I knew where my magnets went to, I'd test the idea right now..
But, since I don't know where mine are off the top of my head.. (but strongly suspect my children have something to do with their absence), I'll just suggest to you to figure this out experimentally: Take one magnet.. bring it closer to a paper clip. Note the distance away at which it will finally attract the paper clip. Now, repeat this with 2 magnets.. then 3, then 4. At some point, I suspect, you'll observe that no matter how many more magnets you add, the distance at which the paper clip is attracted will not increase.
And, if you want some REALLY strong magnets, get some of the neodymium magnets (can be found from several online retailers, and easily found on Ebay)
Magnets are fun toys...
Larger, stronger neodymium magnets are far from toys - you WILL get hurt if you're not careful with them.
Also, if you're willing to do a little bit of work, you might consider making an electromagnet.
Regardless, get a pile of small neodymium magnets.. they're a load of fun to play with!
Oh, and a warning that everyone seems to overlook... if you're playing with neodymium magnets.. even the tiny little ones... DO NOT PUT THEM IN YOUR POCKET THAT YOUR WALLET IS IN!! I have erased every magnetic strip on every credit card, license, etc that I have. Keep them away from the computer monitor.... one neodymium magnet a few inches from the monitor can result in hitting the degauss button approximately a bazillion times to clear up the screen. They make cool fake piercings, but don't pretend that your septum (middle of your nose) is pierced by putting to magnets on opposite sides... otherwise, you'll swear that they magnets ARE piercing your septum from the force they exert on each other... BIG ouch!!!