SNES Cart Electronics
Thanks to Qwertymodo from nesdev forums for being himself:
First of all, capacitors. They are used to filter the voltage supply against variance. Think of them as really small rechargeable batteries. They charge up as soon as the console is turned on, and if the voltage drops temporarily for any reason, those "batteries" help to maintain voltage to the chips. Also, if there are any voltage spikes, they help to filter them out because the spikes get absorbed by the "charging" batteries. This is known as "decoupling". Typically, there will be one large capacitor for the entire board, near the voltage source (the small can looking thing near the Vcc pin on the cart edge), and 1 smaller capacitor near each Vcc pin of each chip on the board. Typical values are >1uF for the large capacitor, and 100nF (0.1uF) for each Vcc pin. Values for decoupling caps aren't critical, you can use pretty much anything that's close to those values. Capacitance values are only really critical when you're dealing with alternating signals or frequency filters. The things that look like resistors but are blue are actually capacitors.
The resistors are typically used as pull-ups or pull-downs. Their purpose is to tie specific pins to either 1 or 0 while limiting the amount of current that flows to that pin. Typically, that will be tied to the /RESET line, pulling up to Vcc. That way, /RESET will be tied to Vcc, which means that it starts out low, then slowly pulls up as the Vcc line stabilizes, so that it will be low when you start up (which holds the chip in its reset state), then when the Vcc line stabilizes, the reset line is released, and the chip is allowed to function. This is typically on the SRAM chip, and the pin is either labeled /RESET (active-low reset) or else CE2 (active-high chip enable), not to be confused with the /CE1 (active-low chip enable). This means the SRAM chip is only enabled when the active-low CE is low and the active-high CE is high. Because these lines are being permanently tied in a single state, you don't want to waste a bunch of current on it, so you want a high resistance value (Ohm's Law, voltage is constant, so high resistor = low current).
The boards without a MAD-1 chip also uses diodes and resistors to handle the battery-backup function.
I forgot to mention, typical pull-up resistor values are 10K-47Kohm. I usually see 10K. If you see a chip that says it has internal "weak pull-up" resistors , "weak" means low current, so high resistance, usually ~56K.