Why do computer circuits tend to have so many resistors and capacitors?
Resistors and caps have thousands of uses.

A couple primary uses for resistors you might see connected directly to the IC pins


Pull up/Pull down (100% a logic function  ;) 
Termination to prevent ringing or signal reflections on high-speed digital signals.  (Computers would not work if this were not done)


Capacitors are used by the bucketload to 'bypass' the power.  When your IC switches logic state (clocks), tons of transistors inside change at the same time.  The result is a little 'gulp' of electricity required.  Because the IC is some distance from the main power supply it can't supply electricity fast enough, you need a secondary supply very close to the IC to prevent the IC from starving for voltage.  The caps right next to the IC's perform this function.   It's alot like a water tower.   The water tower keeps a constant pressure to everybody connected, regardless the instantaneous demand.  If there were no water tower, as demand rises, and you had to pump water miles &amp; miles from some remote reservoir, the resistance of the piping would cause pressure to drop by the time it got to your house.  

There's obviously WAY WAY more complicated matters than the above, but I tried to keep it in simple terms.