Not much at all, a negligible amount, nothing to quibble amount.  Easier to convey with a picture, so lets use one, no two;

We use coffee ground to espresso fineness on a Mini Mazzer as we find changing the grind a pain and the Swissgold coffee filters seem to like a fine grind

And this is what is left in our cup when we get to the bottom.  I know, I can hear you say that it is easy to cheat by swirling the coffee as you go to keep the grains in suspension and prevent them from settling to the bottom of the cup.  We deliberately tried to move the cup as little as possible, leaving it to stand for more than 5 minutes after the water had completely run through the Swissgold coffee filter, then carefully decanting the coffee away, leaving only what you see in the image below.

The point we are trying to make is using espresso grind coffee in a Swissgold filter won't leave you with sludge.

If you are buying pre-ground coffee and perhaps even ground for filter use (much more coarse than this espresso grind shown), yet experiencing unacceptable levels of sludge in the bottom of your cup then the coffee you are using has been crushed at some point after being ground, causing 'fines', or coffee that is almost dust like, much finer than even an espresso grind.

Thinking about it, paradoxically, you may even find that buying espresso ground coffee gives you less fines than a coarse or medium grind especially sold for for plunger/cafetiere/filter coffee use.  Yes, I would actually recommend you try a bag of espresso ground coffee if you are finding unacceptable levels of sludge in the bottom of your cup.  How can this be?  Well coarser grinds of coffee are more likely to crush into powder/fines when dropped/kicked/compressed/generally abused along the path to your coffee cup.  Finer espresso grinds are likely to be small enough to move away from the point of impact, rather than being trapped and breaking up into powder/dust/fines.

To address this issue I would suggest you try to buy coffee sold in a rigid container to protect it from being crushed.  Unfortunately this also rules out vacuum packed 'bricks' of coffee.

Better still, make it a goal to acquire a coffee grinder at some point in 2011 and experience a revelation in your enjoyment and appreciation of just how good coffee can be.