Is it possible to install a bigger HD into an 30gb iPod?

"Yes, you can upgrade to the 80 GB hard drive. You just need a few other parts also:

60/80 GB Headphone Jack

60/80 GB Battery

80 GB Rear Panel

Rubber Bumpers <---forgot about those the first time through

That is all you need to make the swap.

Update

You must replace the Rear Panel because the 80 GB drive is thicker than the 30 GB and your 30 GB rear panel won't fit over the 80 GB drive. Also, this is the same reason you need the 80 GB headphone jack. It has a longer cable to fit around the thicker 80 GB hard drive. This applies to the battery as well."

You almost got it matt- you forgot the rubber bumpers, those are essential, for a complete list of the parts you need check out this wiki page.

A fast and easy way to upgrade your iPod's storage is to get an iFlash mSATA adapter and an mSATA SSD of your choice of capacity. I've done this with my iPod Video and now have 128GB of storage available (more to come down the road!)