If I run Ubuntu on a Dell laptop which was sold with Windows, will that void my warranty?
No it wont void the warranty. You can revert back to windows using the recovery partition or any other recovery media that was supplied with your laptop and your laptop will be back to the state where it was when you bought it. If you are new to Ubuntu and if your laptop comes with recovery partition (which most of laptops these days do) then make sure that you create recovery disks first before installing Ubuntu. Because sometimes people trash their harddisks while installing Linux and that can destroy your recovery partition. Even if you destroy the recovery partition and dont have the recovery disks, you can buy them from dell.
When you send a computer with ubuntu installed for repairs, when it had windows on it, they will take no responsability if they had to re-install windows and remove your ubuntu partition and your data (considering your disk was still ok).
My brother sent his computer for repair because is wifi wasn't working. He got a windows computer back...