First you technically owe sales tax either way. The state can demand you repay it and fine you for ignoring it, but that is rare. Look up sales tax evasion if you don't believe me. Laws on it vary by state. Your concern is whether the merchant will collect it. If they have any physical presence within your state, they collect sales tax. I expect all of them will be required to collect in the near future. These laws really predate the heavy use of electronic ordering processes. I mean you had catalogs and things, but the consumer purchasing volume wasn't anything like online ordering. Today it tends to be stacked against brick and mortar stores, when there should be no difference.
I should mention that in a lot of countries, it's standardized at a national level. Any tax is applied to the stated price as you see it marked whether you're buying it from a store or online. This is generally the case with VAT or GST. I don't think sales tax is generally a good method of taxation, but such a method does make it much easier for retailers. The way it is, businesses have to file separate forms for each state, so the number of required accounting hours is inflated.