I would have built in my custom home a “rain room”: a room with projection screen walls, sound system, and ceiling shower fixtures to duplicate rain in different settings. I might even have a bed in there under a waterproof tarp and pretend I’m camping out on a rainy night.
I just emailed my college friend how I could support her missionary-school work in Sierra Leone. If I got a million dollars, I’d just paypal her 50K or something and let her sort it out.
Oh man a kindred spirit…drool, new socks EVERY day or even every time I fancied changing 'em. 
After donating 10% to charity.
One of these.
Either of these. Hell, a billion? I’ll take both.
http://www.seriouswheels.com/top-2005-Ford-Shelby-GR1-Concept-Aluminum-Body.htm
This specific house. We worked on it, I have been inside and out, love the architecture, location, everything. I’ve seen a lot of really nice shacks through the years, but this one is perfect.
I’d hire a housekeeper and a desk troll. Oh, and someone to keep all my new toys shiny.
Wow, I never realized I was so materialistic…
After donating a bunch of it and setting up a few scholarships, I’d buy a house in our neighbourhood. I would remodel the kitchen completely, with two ovens and two cooktops, and lots of space. And a professional dishwasher, one that cycles through in two minutes.
In the basement or an attached wing I’d set up a soundproof, insulated, high-ceilinged area for Mr. Lissar to use as a quasi-dojo, with mirrors along the walls so I can use it for dance practice.
Does that count as two things? My extravagance is just one house! Oh, and I’d have at least two guest rooms. And central air.
To make it really extravagant, you could just combine the two - ship mountain gorillas to Antarctica and see them there.
(And double-bonus, you’d have your very own unique frozen gorilla ground statuary! It’s a decorating theme that has yet to come into its own, but you could be the pioneer.)
I’d get this handbag. Yeah, $45,000 is a lot for a handbag but I’d carry it until they pried it out of my cold, dead fingers…
Travel. Travel travel travel. I’d just head off with a passport and no real plan and see where I end up. Staying in cute little B&Bs when I feel like it, and ridiculously lavish suites when the mood strikes.
Then I’d come back and find myself the perfect home, not too big, but with a huge lot. The kind of home that gets a name. Antigen Manor or something. In it would be a kitchen much like Baker described. and a library with leather chairs and a gigantic oak desk and a full wall of windows to look out on my lovely estate. The other walls would be floor-to-ceiling bookcases with ladders to get to the high shelves.
You know you can’t start a dream thread like this one and limit people to one extravagance!
Speaking of which, I want a “Lego room”. 
Can a collection count as one extravagance? I’d collect old computers: PDPs of all vintages (1 through 15 with a few gaps, not counting the super-PDP known as the VAX), other minicomputers, supercomputers (CDCs and Crays), mainframes and midrange computers, desktop computers of all vintages, embedded and process control devices, and any other variety I can think of.
I’d also create a super networking cluster, one that would put Google to shame, someplace without much government intervention and host files banned from various places. Nothing I would think of as evil, but, well, that doesn’t leave out a whole lot. All of the files would be downloadable through an anonymous network complete with satellite access into countries with obnoxious censorship régimes. Oh, and it would also have a public access ITS system running on an emulated PDP-10. After all, even lusers deserve their fair share. 
Your extravagance is my necessity. I have all this now.
My extravagance would be a Steely Dan concert just for me and my friends while we are fucked, sucked and blown by a dozen of the best hookers money can buy. (Yes, yes, everybody has to test clean for STDs before getting in the door.)
To quote Greg Giraldo:
Mmmm, ostrich foie gras.