Adding disk space using the VMWare program is like buying a new hard drive, and copying your Ubuntu partition to the new drive; you now have more space, but the partition for the OS is the same size.
Now you can make that partition bigger just like you would with a normal disk. You can run gparted and grow the partition fairly easily. If you've never used it, it's pretty straightforward to do, and if it's not installed already, you can get it from the standard repository.
One thing I forgot is that you can't resize a mounted partition. So, if it's your main installation, you can't really unmount it - you will need to boot the VM from a linux CD that has gparted, such as the live installation CD, and use gparted on the CD to resize the disk in the VM.
Since you installed Ubuntu, you probably know how to boot the VM from a CD (press F2 during boot to get to the "BIOS", and make sure the CD is set as the first bootable drive); but instead of installing the OS, you run gparted, and choose the disk, which should be available as /dev/sda.
Also, since you have the swap file in the middle, you'll need to turn off the swap, delete it, and then add a swap partition at the end. You can create a swap partition at the end of the free space before deleting the current swap, if you're worried about not having a swap file. Probably, though, the swap isn't used during all this.
After some discussion, we discovered one more gotcha. The OS was on a primary partition, but the swap and the extra space was on an extended partition. So, the extended partition needed to be deleted, then the unallocated space shrunk to make room at the end for the swap drive. After this, the main partition is free to grow as a bigger primary partition.