Right now I have a number of LED's and the same number of resistors. I'm thinking about replacing the resistors with a single resistor with high wattage rating. As long as I don't exceed the wattage rating of the resistor I should be fine, right? How will the difference in the LED factor in? Thanks.
Each additional LED you light at the same time, all the LEDs will get dimmer. You'll need higher and higher voltage to overcome the forward drop of each diode.
Also, if the LEDs have different voltage drops, the ones with the lower voltage drops will "steal" current from the others; perhaps to the point of self destruction.
Sorry I didn't make myself clear. I meant to connect all LED's to 595 shift register outputs and have their cathodes connected to an common resistor and then the ground. Will the LEDs dim in this case? Thanks.
Yes.
However, if you're trying to save a little space, you might look at this kind of part: http://search.digikey.com/scripts/DkSearch/dksus.dll?Detail&name=4610X-1-221LF-ND
One common pin, nine equal independent resistors to the other nine pins.
Thanks halley. I meant to save space and somehow I didn't express that in my OP. I'll get some of those resistors.
cathodes connected to an common resistor
If you do that, the LED brightness will vary as you light up more LEDs. In fact, one LED alone will be bright, and then the LEDs will get dimmer as you switch on more of them. There's no shortcut; use one resistor per LED in this sort of application. You can use a SIL or DIL resistor array pack, as shown, or you can use surface-mount resistors. They're not as difficult to solder as people say!
For others who are reading this: avoid connecting LEDs in parallel, because the variations in forward voltage between one LED and the next will cause brightness variations. LEDs in series can work well if the power supply voltage is high enough, but won't gain you very much at 5V. Always install the resistor(s), even if your LED seems to work without one, because otherwise excessive current will flow and that can burn out the LED rather quickly!
Thanks Anachrocomputer. I'll buy some surface mount resistor to play with. Now I have figured out another way. All I need is to have two consecutive LEDs lit at the same time and the rest of them off. I can then shift the position of the lit LEDs to make an animation. As a result, I can hook all even LEDs to R1, and all odd LEDs to R2. So when the setup is working, only one LED on each resistor is lit and the rest are not lit. This way when two neighboring LEDs are lit, they're always on different resistors. ;D