You want a quirky instrument? Try the harmonica! Pocket sized and easy to learn, and they don’t even cost that much. I have a guitar, a harmonica, a fife, a penny whistle and a kazoo, not that i can play them all. Stay away from fifes, they’re bloody impossible.
Dawne hit it on the head. Go with harmonica. 20 minutes a day, and within a month you’ll be playing scales and simple tunes, and working on simple effects. Once you are able to bend notes, the sky’s the limit.
If you want to play along with records, a lot of harp on Dylan, Springsteen, Young, etc. tunes isn’t exactly overly challenging.
I can’t think of another instrument that is as versatile, that you can fit in your pocket.
A fine harp costs $20, and you can get all kinds of music notation and instruction on the net.
Bah, the coolest instruments in the world are the banjo and accordian. Don’t let the naysayers sway you. If you go out in public you are sure to draw attention (see, cool people get attention) and if you leave your accordian on the ground they seem to spontaneously multiply. My friend who plays the accordian told me, “if you leave your accordian in an unlocked car in a bad neighborhood and you come back there will suddenly be two.” It can’t get much cooler than that!
Get a digeridoo. Only two notes, lots of lung capacity, and let’s face it, anything from Australia is cool.
I think pedal-steel guitar is the coolest, but they’re quite expensive.
Bass guitar is satisfying, easy to learn (if done properly), and good bassists are hard to come by, to boot.
Drums are kinda nerdy, really, when played correctly.
I say: Spock Harp.
Whatever you do, don’t play bass.
I want to be in demand as bassist…
Another vote for piano. I’ve always wanted to learn.
Accordeons. Dorkus, is that a tongue in your cheek?
Actually, I have one. I’d like to learn to play but unfortunately it’s imnpossible to play it quietly and I don’t think the people in the adjacent apartments would approve of me rehearsing. What really opened my eyes to the coolness of this instrument was a local band, Polkageist. With an instrumentation consisting of drums, fretless electric bass, accordeon and violin, they manage the standard polka and balkan repertoire, as well as Hancock and Hendrix covers with plenty of jazz on top. The sheer energy of the rhythm section coupled with the virtuosity of especially the accordeon player makes for an act that takes the audience from punk-rock mosh-fest to tears of melancholy in seconds.
But I guess you could do that being a virtuoso on any instrument.
Apart from the coolness of accordeons (when handled properly), consider the points of cost, loudness and portability brought by previous posters. Praqctical matters like that aside, try to find a musician you admire and go for their instrument- it’s great to learn by playing along to your favourite music. Les Claypool got me started on the bass, and though I’ve since tired of Primus I learned a lot from playing their stuff.
Mandolin!!!
I play quite a few instruments and styles of music (rock, jazz, country, bluegrass) and it’s by far my favorite.
In it’s favor:
small
only 4 strings (well, 8, but 4 sets of courses)
cool looking (especially f - styles)
much easier to learn to play melodically than a guitar
same fingerings as a fiddle (okay…violin)
you’ll always get to play at most jam sessions while those fourteen guitarists sit around with their thumb up their ass.
learning to comp on the mando really teaches you how to 1) feel a backbeat and 2) play powerful yet sparse chord structures
It’s really not “just a bluegrass instrument”
Check out some David Grisman…
Piano, you can do all kinds of stuff on one if you want to invest the time. I’ve always been partial to those brown jugs with the XXX on the front too, and the spoons.
Trumpet isn’t a bad one to learn. It’s portable, it’s fairly easy to maintain, it’s versatile, and you can play fun solos. Besides, if you get good at it, you can brag about your ability to double tongue.
forget the bagpipes …
try the uilleann pipes instead! 
I have to agree with look!ninjas on the trumpet. I played for a few years (many years ago), and found it a lot of fun.
Coolest musical instrument? Steinway’s Lagerfeld http://www.steinway.com/steinway/limited_edition/karl_lagerfeld.shtml
But for sheer turn-on value? Let’s just say that any woman who knows her way about a Model D is welcome to have her way with me on top of it.
If you can afford it and have the inclination, a Hammond B-3 organ is about as cool as it gets. Just ask Jimmy Smith or Joey DeFrancesco!
Pipe organ. Not too portable, but then you generally just settle for going somewhere where they already have one. And, potentially, you could wind up playing something the size of a small warship that makes a sound like the wrath of God. How cool is that?
The only instrument I keep gravitating back to, after trying several, is the guitar. I have only two, both by Yamaha, a classical and a knockoff of a Stratocaster electric. I mostly play the classical. However, I have played drums, recorder, melodica, various percussion instruments, bongos, and long ago in childhood piano and violin.
The requirements listed earlier by Kizarvexius plus the fact that the guitar probably ranks highest on the “easy to learn, impossible to master” scale makes it almost required, once you examine its plusses and minuses. That can help explain why it is likely the most popular instrument to own. (I don’t know if that’s really true, but it does seem that way.)
Getting halfway competent accompanying yourself singing or others playing melody is no big deal. Getting to the point of playing chord melodies and other solo guitar etudes can take years of intensive practice. It all depends on how much it matters to you to be able to play convincingly. But for sheer relaxation and self-entertainment, not to mention the physical pleasure of hearing soothing sounds, little else beats a guitar.
Second place would go to harmonica, although it’s not as simple to play as it would appear.
I also agree that if there could only be one instrument for producing the widest variety of music, it would have to be piano. It’s just that pianos are hard to carry.
I’m surprised that no one has mentioned a synthesizer yet.
You can have the versitality of making dozens (or even hundreds) of different sounds, it is always in tune, you can play accompaniment or melody lines, and you can practice with headphones if you don’t want to bother anyone else. They are typically very portable, with the exception that you do always need some sort of stereo or sound system (or headphones).
It’s my opinion that no instrument is cooler than the double-bass, except maybe a steam calliope. But a double-bass is big (though smaller than a steam calliope), expensive, and physically demanding to play.
A violin is a beautiful instrument, but I understand that the learning curve is steep. I don’t play violin, but I’ve listened to others learning, and it can be painful. A beginner on some instruments just sounds like a beginner, but on a violin, a beginner sounds like a cat fight. How much time and effort are you willing to invest?
My favorite instrument is the bass guitar (fretless, but the ordinary kind is fine too). Not as hard to play as the upright, not as hard or as common as the guitar. Bass parts tend to be a little boring when playing alone, though. Personally, I tend to play “lead bass,” which irritates other musicians, but then I mostly just play with myself. Music, I mean.
It may not “musical” enough for you, but hand drums might be worth considering. A good djembe can produce an amazing variety of sounds, and while it isn’t as easy as it looks, you can start sounding okay on a djembe in the time it takes to learn to tune a violin properly. Beating on something with your hands is also a great stress-reliever. The djembe is my favorite drum, but other great choices are doumbeks, congas, and bongos.
Other comments: If you have the right attitude, a banjo or a mandolin can be very cool, but they are a bit limited in application (though it’s true that they aren’t just for bluegrass). Sax is very cool. Flute is somewhat cool, but not as cool as sax, to me. Of course, keyboards force you to understand music better than most anything else, if that’s your goal.
Little FYI here, if you are learning an instrument to be “cool” I doubt you’ll make it past week one. 