i have heard many people saying that their computer slowed down after downloading some program...does it really slow down the computer, downloading programs (or files)?

Every process takes atleast a little bit of memory/processing power. So yes as a matter of these things, downloading will slow your computer, but it should not be anything excesively more than the way running an internet browser slows your computer.
The real slowdown occurs when these downloaded programs are installed, or the download method installs spyware, etc.
The average program makes little difference, but add them up with viruses, spyware/adware, and it's more processor power wasted on things you do not wish to have running.

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even i think so as far as i know . most of the times its the spywares and stuff that get loaded on our computer and hence they unltimately slow the speed of the computer. its always advisable to do virus scan when one thinks that the comp has gone slow

My processor is newish and if i am downlaoding lots of things (im a terrible multi tasker ) then my pc gets really sluggish and cant cope. i think doing any task, like downloading, or having lots of IE pages open or running lots of programs, with it all taking up memory will slow your system down.

Well, your hard drive has to write everything you download. If you are downloading a substantial amount, of course computer will slow down. Every program will wait to read or write to the drive.