I've never had this happen, and I run Mac OS X on a MacBook Pro 5,5 with 4 GB's of RAM (core2duo at 2.33 Ghz). This laptop is from the mid-2009's.
My default set of apps that I run:
1. Safari 2. Mail.app 3. Terminal.app 4. Adium 5. Twitter 6. iCal 7. X11 8. MacVim 9. GitX 10. Activity Monitor
I have no slow-downs and I regularly compile the entire companies code-base on this little machine. Sure it isn't fast compared to some of the newer monsters out there, but I have had no issues with slow downs what so ever.
That being said, I don't use Chrome, and I don't have DropBox on my work laptop.
I keep hearing about people having really bad slow downs and I just don't understand it. Mac OS X has never been anything but "Just Works" for me.
11:29 up 69 days, 17:34, 11 users, load averages: 1.38 1.24 1.18