I'll answer from personal experience, but with a less depressing outlook than other Anon user. Background: early employee at successful tech company, $10+ million at the age of 26.
For me, the first realization was the I never have to work again. The second realization was that I'm not the type of person to retire (ever). I feel as though I've been given the ultimate gift: enough money to do anything, at a young enough age where I still have the time and drive to do it.
Random thoughts, in no particular order:
1/ Net worth is irrelevant, I consider cash flow. Before starting a new company and raising money, I just paid myself a salary from investments. The salary (equivalent to $300k/year pretax) wasn't huge, but definitely affords a life of nice dinners, theater tickets, and frequent travel to exotic locations. That said, it's really not enough to start buying yachts, helicopters, or a brownstone in Manhattan.
Along those lines, my plan for expensive purchases (e.g. a house) is to "borrow" from myself and pay it back from my self-paid salary. The goal is to never even get close to a situation where I could end up broke.
2/ I don't sweat the small stuff. $100 parking tickets, fancy dinners a few times a week, and flights to my college football team a few times per year aren't even worth debating. I don't bother with many traditional financial instruments like life insurance, FSAs, or 401(k)s- it just isn't worth my time for slightly preferential tax treatment on a few thousand dollars per year. I'd rather keep my accounts simple.
3/ I'm terrified of inflation. Given my conservative, sustainable spending habits, the only real threat to me is high inflation. Then again, I don't really care what happens to the United States. If it goes to shit here, I'll just move to Singapore or Hong Kong.
4/ It made me consider what's important in life. Most people spend 40 years chasing money, but that's no longer the driving force in my life. After leaving my company, I talked to many companies in Silicon Valley before deciding I just wasn't passionate about their products. Instead, I traveled for many months and really invested in friendships before coming across the right combination of idea and people that made sense- and now I happily work as hard as ever, with an even greater sense of purpose.
5/ It's true, I'm usually the most underdressed person in the room. Given my age and background, most people just think it's novel and let me get away with it. I figure I can pull that off for another year or two at least.
6/ People ask me for money. It happens, it sucks, and I've always said no. Fortunately, no one really close to me has asked yet- that might be more difficult.
7/ Dating is weird. I don't purposely flaunt money, but when a mid-20s guy takes random trips around the world, pays for expensive meals without flinching, and has a nice flat in a good part of an expensive city; people tend to assume things. It always comes up pretty early, but I try to keep it abstract and avoid specific numbers.
Additionally, it can cause conflict when one person has completely different spending habits than the other. For example (true story), I've had multiple people tell me "that's the most expensive dinner I ever had" - for meals that (by my standards) weren't crazy expensive. Also, the idea of deciding on a Friday to spend the weekend in Vegas, showing up at an airport with nothing packed, and just going is completely foreign to most people.
To top it all off, I'm slightly paranoid about gold diggers. It's also made me compulsive about always using birth control, preferably two methods.
8/ I'm really impatient. I hate waiting in lines or when the subway takes more than a few minutes. I frequently just opt for the taxi, or buy my way into an bar/club with a queue.
9/ I've invested time in learning the most efficient ways to spend money to increase my marginal happiness. http://www.bakadesuyo.com/8-ways-that-money-can-buy-happiness-34746 gives a good overview, but the main point is to buy experiences, not possessions. I own very few things, but have many experiences.
Long story short, the lifestyle probably isn't much different from someone making a few hundred thousand per year in a corporate job. Anything more would involve unsustainable spending habits.
The real benefit is the freedom to do exactly what I want for the rest of my life. That's why I'm happy I have "fuck you" money.