Money. A TLR is the cheapest way to start off in medium format without spending a fortune! There is plenty of choice out there - Rollei, Yashica, Mamiya, Minolta's superb Autocord, even Ricoh and Olympus built TLRs back in the glorious fifties and sixties. The Chinese Seagull is the cheapest really useable TLR, still produced today and marketed under various names. The Russian Lubital TLR is also a possible choice, but a friend of mine in England had one and wasn't very happy with it. (Built by tractor mechanics, optics by the Coca-Cola bottle people, a very substandard offering...)

Simplicity. TLRs are light, simple to load, easy to use, and  a lot less weight to lug around than an equivalent medium format SLR.

Size. 2 ^1/4 square (6x6 cm) negatives give you more than three times the size of 35mm. This means grain-free 8x10 prints on 400 ASA film, and even enormous posters retain excellent sharpness and a full tonal range. Size does matter.

Silence. The mirror doesn't slam up and down at each shot, unlike an SLR, keeping the camera quiet and unobtrusive. The total lack of vibration - all the opening and closing forces within a leaf shutter are expended radially, unlike a vertical or horizontal focal plane shutter -  also means you can hand hold a shot easily at 1/30th of a second, all but impossible with an MF SLR. With practice, 1/15th is possible. This could well be the reason why I've often got consistently better photos with my TLRs than with a much more expensive - and theoretically sharper-lensed  - Hasselblad.  

Flash. TLRs have a leaf shutter that synchronizes at all shutter speeds. Outdoor fill-flash is easy.

Altitude. You can hold the camera upside down, over the heads of a crowd, and still see enough in the viewfinder to compose the photo. Need a bird's eye view of a boxing match? Easier than carrying a step ladder around, eh?

Speed. It is MUCH faster to reload a TLR than to load a MF SLR magazine. My record for a film change with the Rolleiflex is twelve seconds, from last shot fired to cocked and locked on frame one of the next roll. Try that with a Hasselblad!

Discretion. As soon as you hold a regular camera up to your eye, people run for cover: it's pretty  obvious you're about to take a PHOTOGRAPH!  Since you drive a TLR at waist level, people tend either not to notice you as much or not be as nervous. Certainly kids tend to be less shy around that harmless-looking box. 

Control. You can observe your subject during the exposure - who had their eyes closed, who looked away... you can even see the flash going off. An SLR, sharing the same lens for viewing and shooting, flips the mirror up to block your vision at the critical moment of exposure.

Composition. The image in the viewfinder is the right way up but reversed left to right. This is actually an aid to careful composition, forcing you to notice more detail. It's also really easy to check at a glance if everything is lined up straight.

Choices. You have a lot of freedom about how you compose  your shots. The natural format is a square, but of course you can crop the negative for vertical or horizontal format. All options are available to you without your having to rotate the camera - it's a very flexible format!

Angles. A TLR is easy to hold really low, or even at ground level. This can give you a new and unusual viewpoint, and opens creative avenues that would only be possible with an SLR if you were actually to lie down prone! One of my favourite tricks is to kneel and use one knee as a camera rest - rock solid down to 1/8th of a second!

Mechanics. TLRs appeal to photographers who love simplicity and don't want to be dependant on batteries and high-tech. Other than the meter in a Yashicamat or the current Rolleiflex, a TLR doesn't need a single volt to make it work. TLRs are entirely mechanical and generally insensitive to their environment and temperature changes. There's no need to worry about an LCD going black on a hot day or fading out on you in sub-zero temperatures - your TLR will happily click away for you long after modern cameras get packed away safely. 

Longevity. TLRs are generally far more reliable than equivalent medium format SLRs. I've talked to several camera service specialists about this, and they all seem to agree that a TLR's life expectancy - even in heavy use by an overstressed professional - can be measured in decades. There's simply less to go wrong - no mirror mechanism, shock absorbers, bayonet coupling, aperture stop-down, complex film magazine, focal plane shutter, auto-exposure system... all kinds of things that can break just aren't there!

Now I'm not saying they never die. But most TLR problems - and this is true with all cameras and humans, too - stem from lack of exercise! Unused for years, the special lubricants inside will harden and begin to solidify, causing stiff operation and failure. To keep your camera fighting-fit, fire the shutter at least on a monthly basis - run through all speeds from fastest to slowest a few times. Use the self timer if it has one, turn the focusing knob back and forth to squish the grease around, and open and close the aperture a few times. You won't wear it out - if you don't believe me, ask a repair man!

The life expectancy of a Rolleiflex Compur shutter is in excess of 30.000 firings, and the Copal SV found on most Japanese TLRs should be at least as good.  Think that through for a moment: that's two thousand five hundred rolls of 12 exposure film before the shutter will need a check up and overhaul! Join that much 120 roll film together, and you'd have a little over two kilometers of film. Or a hundred rolls a year for 25 years...  then you have an overhaul and service done and run it for another 25 years.

Shoe leather zoom. Other than the Mamiya C range, there are no 6x6 TLRs around with interchangeable lenses. Several companies offered screw-on wide-angle and telephoto adapters, but most folk agree they're not worth the money. Image cut-off with vignetting, a drop in effective aperture and generally poor performance are too high a price for a few millimeters more or less. Use your feet to walk back and forth...
"But I can't change lenses!" did I hear somebody cry out? Great! Just think of the money you'll save by not having to buy any!

Parallax. Just like your left eye sees a slightly different view from your right, the top lens has a higher view than the bottom. It's not much, only about 50mm, and at distances greater than a few feet it's insignificant. But at closer distances, particularly with the bellows-equipped Mamiya, it can be a real problem if you forget about it.

Physics. Mechanical limitations restrict the maximum speed of a leaf shutter to 1/500th of a second. Focal plane SLRs usually go to at least 1/1000th, many medium format SLRs can do better. This may not seem to be a problem until you find yourself with 400 ASA film on a bright sunny day - a couple of extra speeds would help!

Guesstimation. Since the viewing lens doesn't stop down, you have to estimate depth of field using the scale around the focusing knob. Other than one special lens built for the Mamiya and an adapter for the Rolleiflex that's as cheap and easy to obtain as Neil Armstrong's space suit, this applies to all TLRs. You'll have to rely on the engraved scale that most TLRs fortunately have.

Close-ups. Most TLRs only allow you to focus down to about one meter. Apart from the bellows-equipped Mamiya C range, you'll have to use special close-up attachments to photograph anything smaller than a toaster with your TLR.

Printing. Getting prints made from 120 film will be a lot more expensive than with your 35mm camera unless you do your own processing. One hour labs don't do 120 film; it's a professional format which means using a professional lab. It's the same with cars - a big car gives you a more comfortable ride, more space and better performance than a small car, but costs more to run and service.