The rate varies enormously. It depends mostly on how good you are, then secondly what license/insuarance/gear you bring to the job, and finally how difficult the job is. If you're only a beginner climber with a little gear and no insurance then you'll probably only get hired by hacks who are worse than you. Not many people are going to hire a climber who is worse than they are.
In aus, a reasonably good licensed climber with saws and rigging makes about $60/hour, but it's mostly done on a day rate. I know a few hack climbers with no gear who do a days climb for $250, but their 'day' is really only equal to a couple hours from a good climber. Most good climbers do something more like $350 for a half day, $550 for a full day.
I don't do much contract climbing because it doesnt pay as well as doing my own jobs. I won't climb for people I don't know any more, and I don't do a day rate any more either. I charge by the job, just like I do for my own jobs. There's a few guys I do regular work for, they know my prices are fair, and I know I'm not going to have problems when I turn up. For me, that means they have their own gear, are licensed and insured, have enough ground staff, have a permit for the tree and are realistic when they tell me how many hours they need me for.
Shaun