I have iTunes 7.6 and my iPod touch jailbroken on 1.1.3 with the January Update for free, and every time I plug my iPod into my computer, the iPod shows up in the list on the left, and before I can do anything, it loads up a January Update page, which it let's me select "No Thanks", "Remind Me Later", and to buy it. When I click "No Thanks" or "Remind Me Later" iTunes throws a fit about the music store having an error about not being able to process the request, which then throws me to the main iPod screen so I can sync and all that good stuff.

How do I get around this?

You are in a better situation than me...
I'm in a country that doesn't have a local iTunes store and Apple doesn't accept my credit card, so there is no way for me to buy the upgrade even if I wanted. Worst, when I plug the iPod, it doesn't matter which button I press between "No thanks" and "Remind me later", iTunes gives me the same upgrade advertisement and no way to display my iPod's content.
I was wondering if there's any way around it... The only thing I could think of (and it worked!) was to turn my Airport reception off. But that is not so elegant, less coming from Apple.
Any thoughts?

I'm having the same problem!

I used Little Snitch to stop iTunes from accessing the internet, which lets me now access my iPod touch's settings. Other than that, there's not much else to be done. The downside is that I cannot get to the music store to download album art, but half the time it never grabs the right artwork anyway...