My Laptop has 768MB RAM and a Pentium-M 2.00 GHz processor. Can I use Ubuntu 12.04 on my Laptop? Will it slow down?
Yes, you meet the system requirements for Ubuntu.
but it wont be fast, I would suggest you try something like Lubuntu.
Lastly this is up to you if you feel it's fast enough, try out the system you want with a live usb, that will give a feeling of how fast it will be.