In California, you were, in theory, required to pay a "use tax" on any goods purchased from out-of state, that just happened to be equal to sales tax. The reality is that most consumers didn't do this, since the only way to get caught would be if they audited your return.
On top of that, if you maintained a commercial presence in the state you are shipping to, sales tax was required. So, any national retailer that also sells online had to charge sales tax.
Amazon was in a gray area where they had shipping warehouses, but not commercial offices in California. They ended up making some deal a couple of years ago where they would charge sales tax online. I'm not sure what Amazon got out of it though.
So you used to be able to illegally get away with buying online without sales tax in some circumstances, but it is no longer the case for Amazon.
Specifically, by default, mail order stores are not required to collect sales tax unless the have a physical presence in the state (retail store, sales office, distribution center, etc.) Quill Corp. v. North Dakota from 1992 is the major SCOTUS case law.
In theory--at least in most states with sales tax--residents are supposed to pay a use tax on out-of-state purchases bought to be used in their state of residence.
A number of states have put pressure on online retailers like Amazon to collect. One of their levers has been to argue that Amazon Associates constitute a physical presence. And Amazon has agreed to collect sales tax (although not for affiliate sales) in several states. Massachusetts for one.
Online shops aren't required to collect sales tax unless they do business in the state that they're delivering to. If a company only exists in California, then only California residents have to pay sales tax. Amazon has warehouses or offices in most states.
