I'm using the latest version and installed it on my desktop, memorized my seed phrase, set my password and moved some coins into my wallet.
Are you sure you will remember your seed phrase forever?
You should never rely on memory. Keep your seed phrase somewhere safe. It's even recommended to have multiple copies of your seed phrase in different location.
Why is this? If my computer gets stolen all anyone needs to do is crack my password and they get my coins. I want to remove any trace that Electrum was ever on my computer. Can somebody tell me how to do this please?
As stated by above by Zaguru12, you should delete the wallet file.
Where is the Electrum datadir located?It may worth mentioning that deleted file may be still recoverable after they are deleted.