files to put in another partition

You can symlink folders to other folders on other partitions. It can get messy but is possible. We may be able to recover space for you. Can you give the output of:

lsb_release -a; uname -a; dpkg -l | grep linux-image-

Thanks

In Unix, you can mount many partitions on file tree. E.g. I have /home folder on a dedicated partition. It's better to move a whole folder on a new partition. Could you explain more your problem.

My root for Ubuntu is on a 10Gb partition. I have another 190Gb partition. All downloads, new programs, updates, etc. all go on the 10Gig partition. I would rather they went into the 190Gig partition. So, it's a two part question. How do I get those files over onto the 190Gig partition, and how do I keep this from occurring again?

If you can give the output of the command I gave, I may be able to get some space back for you

An easier way should be to resize partitions, i.e. extend 10GB partition to 20GB and reduce 190GB to 180GB. You will have less issue than by making a complex file system.
For this, you can boot on Ubuntu CD, choose "Try", open a terminal (Ctrl+Alt+T) and run "gksudo gparted".

Perhaps you have also useless files in "/" partitions, like old Linux kernels (so please answer Andrew question) or old downloaded packets. Could you run:
   lsb_release -a; uname -a; dpkg -l | grep linux-image- for Andrew
and
   cd /var; sudo du -s * | sort -n
and post results.
You can also use
   baobab
to analyze disk usage.

Here's the output:
No LSB modules are available.
Distributor ID: Ubuntu
Description: Ubuntu 10.10
Release: 10.10
Codename: maverick
Linux knromine-Dimension-3000 2.6.35-30-generic #61-Ubuntu SMP Tue Oct 11 15:29:15 UTC 2011 i686 GNU/Linux
ii linux-image-2.6.35-22-generic 2.6.35-22.35 Linux kernel image for version 2.6.35 on x86/x86_64
ii linux-image-2.6.35-30-generic 2.6.35-30.61 Linux kernel image for version 2.6.35 on x86/x86_64
ii linux-image-generic 2.6.35.30.39 Generic Linux kernel image

sudo apt-get --purge remove linux-image-2.6.35-22-generic; sudo apt-get --purge autoremove; sudo apt-get clean

Will get you about 120Mb of space

120Mb or 120Gb?

Mb or Megabytes

You can use bleachbit to clean out temp stuff you don't need. Close as many apps as you can. Run it as user and root. Avoid options saying they will take a long time and watch your options or it will remove data/settings you want to keep

bash: cd/var: No such file or directory
du: invalid option -- '*'

cd /var; sudo du -s * | sort -n
Please do a copy/paste with Ctrl+C on FIrefox and Shift+Ctrl+V on terminal to avoid typo.

0 lock
4 local
4 mail
8 games
24 opt
216 spool
224 run
5304 backups
5492 tmp
7324 log
280680 lib
290168 cache

You have only 600MB in "/var" folder.
To empty /var/cache/apt use "sudo apt-get clean" ( https://help.ubuntu.com/community/AptGet/Howto#Maintenance_commands )
Then rerun
   cd /var; sudo du -s * | sort -n
to see how many space was recovered.
Could you provide result of command:
   df