I should also note that we're not in the middle of any big projects at the moment, so I'm not holding any previous work I've done hostage. All big projects have been completed & delivered.
If the client is an established business, don't fret: vendors changing rates is a normal part of business. Just inform them that as of X date, your new rate for consulting work is XXX per hour and ask them to confirm receipt of that email in writing. I'd say that 2 weeks advance notice of the rate change would be more than sufficiently courteous.
If the client is just one guy or something, I'd say that raising rates would be fine too: but maybe give them a bit more lead-time on the change: maybe closer to a month advance notice or something and make a point of mentioning that you're giving him extra time to prepare. And as always, get confirmation of the rate change in writing.
As gostsamo wrote, ask if they're interested in continuing. If they are, here's an example of what you could say next: "I've really enjoyed working with you and I'd love to continue. I'd be most comfortable with $100/hr. Would you consider that at this point?"