Resistors for multiple LED's in parallel?

I'm building a snakebot, with RGB LED's in each link. The number of links is variable. I plan to run three PWM lines through NPN transistors to drive them. Do I need resistors in series? Normally I'd use them & size them for the current draw, but I'm not sure how much current a varying number of LED's in parallel will draw...

In general each LED should have it's own current limiting resistor. It would be unusual to have LEDs with exactly the same drop across them so they would not "share" the current properly (and different colors have different voltage drops). You can have multiple LEDs in series if your supply voltage is high enough, but you still need a current limit in series with the string to limit them to the desired current.

Do I need resistors in series?

Yes.

Normally I'd use them & size them for the current draw,

Correct.

but I'm not sure how much current a varying number of LED's in parallel will draw.

That is not an issue, you have each resistor and LED in series so the resistor only controls one LED, you can't have LEDs in parallel, they need a resistor each.

Sooner or later, you will come across a diagram showing LEDs in parallel. The thing to keep in mind when you see this, is that such circuits use diodes from the same factory production run. Hence the characteristics are almost identical. A lot of the larger 7 segment displays use series/parallel combinations. But it doesn't mean that you can do it with off the shelf components.