Seems like a fun idea, I'll have a go. In no particular order:
Lamborghini Miura SV - The Miura is arguably one of the most beautiful cars ever made. The looks alone make it a stunning car. But add a 385 bhp 4.0 litre V12 mounted right behind the driver, and I imagine it to be an incredible experience to drive. Jay Leno daily drove one for years!
Jaguar E-Type - The E-Type is also a gorgeous car. It too has a gem of an engine, a flexible and sonorous straight 6. It handles impeccably and is more comfortable than many modern luxury cars, yet can dissect a twisty road with precision, speed, and character.
Ferrari F40 - The F40 is one of the most visceral, raw, and insane cars ever built. It's notoriously hard to drive, and very fast. And for the sheer driving thrill it earns a place in my garage.
MG TC - It's not as prestigious as the others, but I think it's just as pretty and is terrific to drive. It's simple and wonderful.
Aston Martin V12 Vantage - I'm a massive Aston fan, and the V12 Vantage is one of my favourites. It's gorgeous, has a V12, and a manual gearbox, all in a terrific chassis.
Aston Martin DB5 - Yep, another Aston. This one is quite similar to the E-Type in some ways. A classic British GT with gorgeous lines. When you see one you feel a need to sit in the driver's seat. I don't actually like the Bond connotation because I'm no James Bond, but I'd not let that stop me.
Singer 911 - Arguably, the Porsche 911 is the ultimate incarnation of the sports car. And the Singer is arguably the ultimate classic 911. It's gorgeous to look at, with the whole car being basically bespoke, and it drives like a gem.
Ferrari 250 GT SWB Berlinetta - What more needs to be said about this one? If nothing else, look at what else I picked and it fits right in.
Morgan 3 Wheeler - Fun. Pure fun.
Caterham 7 - This one's for the driving enjoyment. Not really that bothered about the model, but I'd like one with 160-220 bhp, manual gearbox, and most of the performance hardware, but road tyres. Perhaps a Supersport R.
You don't have to be terribly astute to notice a theme. There's only one truly modern car on the list in the form of the V12 Vantage, while the Morgan, Caterham, and Singer are all modernised versions of classics. They're all European, but let's not forget that the Americans and Japanese are just as good at making truly great, fun, and beautiful cars as the Europeans. It's all a matter of taste. And that said, I don't think there's a dream garage here I wouldn't be thrilled to own. There's so many cars I want to own that I could easily think up a completely different 10 car garage that I'd be just as happy to own.
Oh, and one other thing I just noticed but sort of knew: they all put more emphasis on the driving experience than outright speed. They're not the quickest on a track (Caterham possibly excluded), but ooze character and would be a true motoring experience.