I know this is somewhat bass ackwards and that most will say V-12 or V8, or inline 6. I however seem to always gravitate to inline 4 cylinder. I'm not sure why, maybe because almost all of my first cars were? Maybe it's the lighter front end and I prefer non power steering cars, such as Alfa's, early Volvo's, ( my first 6 cars I grew up with)? But to me that is the beauty of them. It isn't just the motor but the cars designed around that too.
My faves have always been in line 6 or V-12, and I've owned them all. Well that's not quite right, I haven't had a 5 or a 10 cylinder yet.
V8
Rotary
I've never owned a V8, but I have had a few V6s and I've continuously owned 4 cylinder cars since 1976. I prefer small, light cars and the sound of a raspy four.
Inline 6! Nothing sounds or feels as good, at least to me. 
2nd choice V12, which is two inline 6s. However any V engine is much harder to access for maintenance unless it's in a bus or something really big like that.
Having said that, it's obvious from my avatar that I do also enjoy an inline 4. In fact all three of my current cars are inline 4s with stick shifts. Which brings up another issue entirely. I have three stick shift cars & each one has reverse in a different position in the shift pattern. We're still fighting gear pattern choices, including where to put reverse, after all these years.
When autocrossing I always wanted 1st and 2nd to be inline for that first quick shift. Then usually into 3rd for the rest of the lap. But when road racing a 5 speed, I always wanted reverse to be above 1st so that 4th and 5th were in line on the far right gate. And with six speeds, reverse seems to be almost anywhere.
I love twin-cam inline fours. Especially with ITBs or Webers. The sound at WOT is awesome.
Flat 6.
Ya' know, I have never driven a V12 myself and that got me thinking....the only inline 6's I have ever driven were old Plymouth slant 6's and long ago my grandmothers '68 Ford Fairlane.
I looove the sound and smooth feel of inline 5 cylinders.
Inline 6 is a close second, but I imagine if I had driven a 12 cylinder, flat, V or W, the order might change.
I only drove a V-12 once, telephone poles were clicking by and I didn't realize how fast I was going. Right, no self control.
Inline six, they can be prettied up with bronze freeze plugs and six Strombergs.
2nd choice: flat head straight eight.
Back in the day my dd was a Valiant w/slant 6. Seven main bearings. Drove it WOT whenever possible for over a year and shifted when it would not go faster. I also worked on Jags w/straight 6 and V12. This was when domestic engines were going thru early emissions woes and idled rough. Not the Jags. Smooth and fast. Awesome sound! Owned several muscle cars and Corvettes w/rumbling/roaring V8s. Inline 4s, V/4, flat 4s, even a 3cyl 2 stroke. Favorite: small block V8 w/inline 6 2nd
V8s for me of course.
I own three V8s and one inline 4 car/truckwise.
Rotary, Flat 6, Inline 6, and Pushrod V8 
The Inline 8. There's just something intrinsically cool about them, which is good, given how heavy most of them are. The V16 is on that list ipso facto.
I love two stroke twins; my first experience with performance were Yamaha RDs, between these and TZ250s just sound great to me. I wish my F500 had twin expansion chambers, not for performance but the sound.
V12 Ferraris sound almost surreal, hard not to love them.
I'm on board with inline 5, group B Quattro anyone?
For me though the most raucous sound ever is Honda's 5 cylinder 125 GP bike (RC146 I think) there is a You Tube video of them warming one up, just incredible. (OK found it)
https://m.youtube.com/watch?v=Xuvx15DLDmc
Nissan makes a twin cam triple I'd love to put in the Datsun as it would sound cool.
Tom
V8 with a Quadrajet.
My favorite motor configuration is one that runs......and runs well. 
My favorite is an inline 6. I'd like to say a V12, but the only one I've driven is an early '70's Jaguar and it didn't seem all that impressive.
Assembled and running.
In reply to Tom1200:
With that video, I at first wondered: how will we know when the bike is started because of that barely-muffled 1-pot starter thingy? Then the bike started 
Then I saw that the tach goes to 22 
Back on topic : I've had a car with an NA I-5, then a car with a turbo I-4 (that I swapped in), then another car with a turbo I-4, then a car with an NA I-4 that revved to 9,000rpm, then a car with a turbo Flat-4. But my favorite is Inline-6 
... or flat-6.
I am a small block Ford guy, all the way.
i like v6s, i6s, and inline 4s the most.
Of that I heard the Alfa or Genesis V6 sounds the best, the RB series and L series (with side drafts) for i6, and inline 4s Fiat Twin Cam or S2000.
I'm sure there are better sounding ones than those that I haven't heard.
After those I like V10s and V8s. Every V10 i've heard sounds good probably because people don't usually berkeley up the exhaust on cars like that like people do with V8.
Inline 6 and 4 are my favorite to own because I like working on them.
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