I am going to Arizona in a few months and plan filming some of my rounds of golf. Other than a UV filter, should I use any other type of filter with my GL2?

A grad ND filter might darken the sky down a bit.
A grad ND is a .6 neutral density at the top and gradually blends into plain glass at the bottom. It tones the sky down by 2 stops. Usually you either have the landscape exposed correctly and blow the sky out or if the sky is exposed correctly then the landscape is too dark. In the desert, the contrast seems a lot greater. Tiffen make this filter in a few colors and ND.

A linear polarizer might be needed if you're going to be dealing with anything that might produce glare. They also deepen the color of water, sky and foliage.
http://www.tiffen.com/color_grad_filters_pics.htm

Be sure to take a tripod or at the very least a monopod. Arizon is beautiful and given the recent rain the desert will be in bloom. I was there two weeks ago and it rained the whole 5 days.

I'm headed to the Tucson area the end of this month. Been told to expect a little wetter than normal. Plan on going up into the hills for a few days of shooting.

1. a polarizer
2. a grad ND filter is a good idea, a blue grad filter might look great too. Enrich and darken the sky.
3. a hat that covers the back of your neck so it doesn't get sunburned looking into the viewfinder.
4. definitely a tripod so you can set up shots of yourself golfing

Mostly the same advice as Brian, but it's worth repeating.

Last summer and fall while I was shooting stuff here in the beautiful Rocky Mountains, I noticed things just looked much nicer through my sunglasses (rose/brown combo) than they did in real life... the grass greener, sky bluer, changing leaves brighter, more vibrant, etc. So I got the bright idea to go to the optomitrist who made my sunglasses and ask him to tint me a filter the same color. He did. Twenty bucks. Awesome footage!

lol. charles. good idea.

Seems like people like Tucson. Ya, been here over 30 years.

Will never leave.

Bob