OP just popped on to comment.
I have 2 pugs, both 9 and 10. One has had no health problems at all, the other has suffered mast cell tumours (benign and low grade) frequently in the most recent years. The one who suffers these tumours was the runt of litter, and perhaps I made a mistake in picking her as because she was so very fiesty after being cared for by the breeder and hand fed and cared for - she passed all her health checks. Mast cell tumours are not breed specific, they are common in a whole host of dog breeds.
People of MN don't like Pugs. They call them fashionable and designer but they have been around 100's and 100's of years, though like all dogs they have been changed as they have bred out. Half the problems listed here are people taking the most common ailments and applying it to all.
All dogs have problems. Great Danes, bloat. Cockers have a rage thing. Sharpei, skin problems and allergies, chihuahuas... well... snappy and nervous. Look up any breed and theirs a list of problems.
So here's my breakdown from my own experience.
Breathing: both of mine breath perfectly. They won't be going with me on a run but they breath fine and dandy and not laboured. They snore sometimes but really depends on what positing they fall asleep in. They do get hot so on days when it's above a certain temp in summer we skip our walk - no one really complains. They play, run about and do dog things with no problems.
Eyes: both fine. No problems in the last 10 years. They have a pigment issue which may cause problems but nothing other old dogs won't have issues with. Face flaps - one of mine rarely needs it doing. The other has deep folds which requires wiping once a week with a wipe (box lasts flipping ages and not expensive), and drying with kitchen roll after.
Teeth: they don't have many left now, but still crunch their way through a carrot each evening.
Hair: lord the hair. Furminator brush and shampoo/conditioner. It will save your sanity. Pets at home grooming parlours offer this service, I take mine every 6 weeks and wear a lot of grey when she's shedding. But regular grooming is a must. It takes 10mins once a week with the brush with regular shampoos.
Black pugs shed considerably less than fawn pugs. Fawns have an undercoat whereas black ones do not. It does come in cycles though as a PP has said.
Personality: gorgeous beautiful dogs. Wonderful around children despite not being in regular contact with them. Funny and loving, they're going to steal your heart and everyone who meets them.
Exercise: when younger they went 20mins twice a day. Now their old they aren't that interested and run for the sofa but will still go for 20mins a day and longer on weekends (45mins or so). They don't get irritable if it's bad weather and we don't go for a few days - mine don't really like the rain so I don't torture us.
Weight. The little one has 35g of food with 1/4 a pouch of wet food, (she is 6kg), the big one has 45g of dry food with 1/4 pouch of wet (he's 9kg). Twice a day. They are predisposed to gain weight and I'm very strict on them not having treats daily (hence carrot). But if you buy a good quality food they won't go hungry and with exercise they won't gain weight. ALL dogs get fat if you over feed and don't exercise. Less exercise? Less food. This really isn't a breed specific thing just common sense... but with pugs you do need to be a bit stricter as they just don't burn it off.
It is pot luck health wise with any dog you get. Take a good look around the breeders and keep in mind people will only tell you the horror stories/bad things - especially on an Internet forum where you most probably won't have a balanced view. As I've said MN hates so called 'designer' dogs, you have Pug in the title and this will naturally draw people who disagree with the breed to comment.
Enjoy visiting the puppies, they are scrumptious balls of squish! Feel free to PM if you have any questions.