you should add a little gate resistor also, try 100 Ω to limit inrush as the gate is very sensitive. Never leave it floating so if you're using an N Channel you will want a pull down.
Ok, so if I want to use a 3.3v MCU, then I'd need to use a PNP transistor like a 2N3906 to switch the 12v nominal to the gate? That TI MOSFET says it's ok with 20v gate-to-source, so I guess it'd still be ok?Thanks for the help.
You are very unlikely to find a 3.3V rated MOSFET except in a surface mount package.