Vacuum line to the EGR or "Combi" valve I believe...

 

It looks like the vacuum hose to the Combi valve. It's not an EGR valve--our cars don't have an EGR--rather, the combi valve opens to allow fresh air from the secondary air injection pump (SAIP), aka smog pump (a blower, really), to pass through the catalytic converter (cat) after a cold start. That heats the cat up quicker so it starts working sooner, reducing pollution. Without that vacuum hose, you'll get a P0411 fault code.

I changed the hoses to silicone on my car, blue (just because), since they get hard and break (as you know). Here's what my car looks like (photo below); the text points out the coolant temperature sensor location. See my vacuum hose DIY for more detail: http://www.passatworld.com/forums/61-b5-information-base/337838-diy-how-replace-1-8t-awm-vacuum-hoses.html

 

Thanks for the info, my car is actually a V6 so I imagine the hoses would be slightly different. Good to know that I'm not the only one with this annoying problem

 

Slightly different, yes... you have two combi valves and a tee in the line that feeds them.

May your vacuum hoses always be pliable and leak free...