How can I disable the purple splash screen at boot?

Quote from /usr/share/doc/plymouth/README.Debian (from package plymouth version 0.8.2-2ubuntu2, which is the one installed on Ubuntu 10.04):

There are two methods to disable the splash screen. Both have the same effect. Your boot will show such messages as are emitted by the starting services, and will still be able to prompt if needs be.

1. Remove all of the plymouth-theme-* packages from your system, including the text ones. Plymouth will remain installed to permit boot-time prompts.

2. Remove splash from the kernel command-line. You can do this per-boot, or make it permanent by changing the GRUB_CMDLINE_LINUX_DEFAULT line in /etc/default/grub.

The second method also requires running update-grub as superuser, after editing that file.

Temporarily disable splash

You can edit the boot entries in the menu from within GRUB to temporarily disable the splash screen.

Try the following: Select the entry, press the key to edit this entry (it should be e), go to the kernel/linux line and remove quiet splash, then press F10 to boot.

Here are two screenshots from a VM to show you how it should look like:

Permanently disable splash

The permanent equivalent was already quoted in Riccardo Murri's answer:

2. Remove splash from the kernel command-line. You can do this per-boot, or make it permanent by changing the GRUB_CMDLINE_LINUX_DEFAULT line in /etc/default/grub.

... followed by update-grub as superuser.