You don't specify an amount, so I'm just going off a few Million as most of the US big lotteris start around $10 million and after taxes, it's about half or less. For myself, I'd pay off all my debt and then buy a couple hundred acres in very rural area and build a small house on it. This would be my outdoor playground so I can enjoy the outdoors with very few people around. From there, I'd invest enough to live comfortable off the interest until I die. I wouldn't change too much in my current lifestyle. About the only thing I might change is travel a little more and visit the places I want such as Australia & New Zealand, Europe and a good portion of the US I haven't already seen.
After that's setup, I'd give to my closest friends to pay off/down their debts and make their lives a little easier. Finally, I'd donate to a couple of charities that are important to me.