I am wiring my basement. All the outlets are running off 2 independent 20 amp circuit breakers connected to each other by 12/2 wire.

I wanted to run some stubs off my 12/2 outlets. All each stub would do is run to a small light (max 180 watts) and of course a light switch. Since I ran out of 12/2, is it crazy to run the wire to the light and the light switch using 14/2 gauge wire?

This means that the short stub of 14/2 shares the same 20 amp breaker as the 12/2 circuit.

Is this safe? Is it code?

No, what you propose is not allowed, nor safe.

You would then have # 14 cables protected with a 20A breaker. Won't fly and as tk said, is very unsafe. You would have to install a 15A breaker and that may not meet code either depending on the circuits. Plus, it's not considered good workmanship.