Low-impact exercises
- swimming or water aerobics
- the eliptical machine
- spinning (cycling indoors)
- the rowing machine (this one is great, as it focuses on your upper body)
- hula-hooping (burns mad calories!) - you have to buy a good, heavy hoop though
- strength-training
- yoga
- pilates

You should be doing strength training if you want to lose weight. It increase your muscle mass, and muscle burns more calories than fat. If you increase your muscle mass, you will be burning calories all day -- not just while you are excercising. Basically, by strength-training, you will increase your metabolism. Go get some free weights and do upper body exercises. You can also do a bunch of excercises on the floor, like abdominal crunches, without putting pressure on your feet.

Finally, make sure that your gout and arthritis is well-treated with medication. Don't be afraid to take pain meds if you need them!