Is UK internet = US internet ?

I don't know if the technology has changed (mine was a couple of years ago), but no -- the thing literally acts like a remote control on the cable box. You tape a little infrared thingie to the cable box and everything. Then it intercepts that signal and gets it out on the internet.

When I moved, I didn't bother trying to stick my parents with it. I doubt I'd want to watch what they're watching 

If you've got the know-how and slightly skewed sense of morality you could always telnet through random US users, masking your IP with theirs, allowing you to then access things like hulu and other media.

does this mean I should have brought my US router with me... because that can be used as a US proxy?   (not sure)..   

No it won't help.

 - Because your IP address is assigned by your ISP when you connect, so it will still show as a U.K.-based IP address, regardless of the originally intended market of the router.  Everything else which can be used to try and find out where you're located will be in the packets of data coming from your computer anyway, and that data is not modified by the router.

I've had fairly good results with Hotspotshield lately (anchorfree.com). It's a free browser plugin that masks your IP origin. It's come up on UK-Y before, though I don't remember who first recommended it.

I gave up on it first time, because Hulu was intolerably laggy and had buffer problems with it. I've subsequently learned that this is a symptom of time of day. If you watch during US off-peak hours, you get better results.

We don't have a cable boxes at out house, but we do have cable jacks in every room, so couldn't I just plug it into the jack in my bedroom and it wouldn't affect the other TVs?

I'm not sure about slingboxes, but you could get a cheap computer and set it up as a DVR. You'll need to buy one or two TV input cards, but it works directly off of the cable (I'm doing this currently).

When I moved, I didn't bother trying to stick my parents with it. I doubt I'd want to watch what they're watching 

That's the very reason that ours is on an unused TV.  Although every once in a while, I can tell my dad has been watching the TV that the slingbox is hooked to (well, the TV attached to the cable box that the slingbox is hooked up to) because it'll be on ESPN and there's no chance I'd have turned that on voluntarily.   

I'm pretty sure that the cablebox is a necessity for the slingbox to work.  We have it hooked up to a DVR cable box, which has been enormously handy.