unless you signed a "at will paper", which means you can quit or be fired at will. no notice needed then.
2 weeks notice is the norm so your old job has some time to replace you. but on the flip side, ive never been given 2 weeks to find another job, always sent packing if fired. or laid off on a Monday with no notice.
my last job forced my hand and i walked the F out on them, flat, and i got unemployment even after they tried denied my claim. and i had a at will paper that they had me sign.