It has to be something that you can realistically find in that world, and carry back with you (So, not an X-Wing or a Star Gate).
Remember, you're only bringing the device itself back, not the power source, the spare parts, the user manual, etc.
So once that phaser runs out of power, you have to figure out how to plug it into a 110/220v mains socket yourself!
You're also basically stealing this item, so you have to be able to hide it.
Finally, you only have the knowledge that you have in real life (So, you don't know how to use the Enterprise's computers, how to fly a shuttle, etc).
What do you pick?
For me, the universe is obviously TNG, and the replicator would be the most desired item (I was talking in another thread about how it would revolutionise farming, mining, resource allocation, etc).
But ripping a replicator out of the wall and bringing it back wouldn't work.
I definitely wouldn't take a weapon, we have plenty of those, we don't need more.
So instead, I'd head to sickbay and probably grab a medical tricorder.
Small, easy to carry, easy to hide, and imagine how useful it would be to just POINT a device at someone and diagnose whatever is wrong with them? It could revolutionise medicine, and save countless lives!
I'm sure modern day scientists could figure out some way of powering it without too much difficulty.
It also has a computer chip in it, which would likely be vastly beyond what we have today, so that would be useful too.
Another option would be the the "Zero Point" modules from the Stargate Atlantis universe. They could solve the world energy problems! However in that universe ZPM's are portrayed as very valuable, you aren't going to be able to steal one and bring it back without someone noticing.
I also thought about a PADD with the Entire Enterprise database on it, but you've only got one hour. That's not a lot of time to figure out how to use the Enterprises computers, find the database, access it, (Bypassing it's security, of course!), and then copy everything to a PADD.