As far as I recall there are a few things that complicate it in America:
1) GSM vs CDMA phones.
2) Supported GSM bands
3) Carrier restrictions.
An 'sim-free' or 'unlocked' GSM phone, like the Streak, should in principle work on any GSM network that uses the band frequencies listed in its manual. In the case of the Streak it's quad-band on 1900/1800/900/850 Mhz Frequencies so I would imagine as long as your provider is a GSM provider, and uses one of these, you're fine.
The third is trickier. I have heard of some American service providers who restrict devices, in the same way you restrict devices on your home wifi. Thus it would be the provider who needs to be contacted.
In short: Yes, unlocked should mean 'unlocked', but there are other things to consider. Can't take a GSM phone and use it on a CDMA service like, presumably, verizon. (I know not who does CDMA in the states, in the UK everything is GSM)