- Akane, Ryoga, Ranma, Kodachi, Ukyo, Shampoo, and Mousse are 16
- Gosunkugi is 15
- Nabiki, Tatewaki are 17
- Kasumi is 19
- Tofu, Hinako are in there mid to late 20's
- Soun, Genma, Ranma's mom, Principal Kuno mid 40's
- Happosai, Cologne - something over 100
Let's start with the Kuno's.First we know that Kodachi is younger than her brother Tatewaki and in high school so a good guess would be 16. Is that her age though? I don't know it is possible for Kodachi to be 15 and have just skipped a grade at some point or just is in the age bracket where she will turn 16 sometime during the school year. Tatewaki's age of 17 is not given in the manga until the second half of the manga during the mushrooms of aging arc (in the anime I believe it is given during his intro).
Shampoo and Mousse are 16 or are they? Simple put we are not given any clues as to their age. Shampoo and Mousse can easily be 18 or 20 there simple is nothing that says they are the same age as Akane.
Ranma's mom, Genma, and Soun again who knows. Ranma's mom could be in her 30's (marriage age when she could have had Ranma was 13 after all - before 1995 the marriage age for girls was 13), Genma could be in his fifties since martial arts could slow down the aging process some, etc. All we know for sure is that they are at least 30 years old.
Let's do Ryoga know. Like most of the characters we have no absolute way of knowing though 16 is a good guess. Judging by Ranma and Ryoga having attended the same school together (we do not know if they were in the same grade) it is likely that Ryoga is within 2 years of Ranma's age, though during the mushrooms of aging arc Ryoga thinks himself to be 16 at that point in time (but Ryoga may not be the most reliable person to know his age since he commonly gets lost for weeks at a time).
Happosai and Cologne's age can not even be guessed at. We know that they are really old but how old can't tell. It is entirely possible that Happosai is 120, 300, or even older. Why is it possible for Happosai to be hundreds of years old? For these reasons, Martial arts may slow down the aging process some, Happosai has access to age altering magics (Jusenkyo, rejuvenation potion - others exist like the mushrooms of aging) and age altering techniques (whatever Happosai did to Hinako). Not counting the use of magic or age altering techniques Happosai can still be positively ancient when you consider that Happosai can somehow survive for years without food, water, air, and female undergarments. It is entirely possible that Happosai did like some mythical dragons and slept for a century or two. That is for the manga. For the anime we know that Happosai and Cologne are at least 300 since that is the amount of time traveled back into the past via the Nabian mirror but it is entirely possible that they are even older than that. According to wikipedia: In the anime episode "Case of the Missing Takoyaki!", Happosai's age is given as being estimated at four-hundred and fifty (450) years old. While most consider that to be a mistake on the part of the anime writers it's not impossible for him to be that old since he could have used something that made him younger prior to the time he met Cologne.
Alright I've basically stated that we know for sure only a few characters ages. Think Ranma is one of them. Think again. Anime Ranma is 16, we know that for sure since the Anime straight out says it. What about Manga Ranma? He's 16 too right. Maybe, Maybe not. Ranma thinks at least by the time of the magic mushrooms that he is 16. It is possible, even likely, that Ranma was 15 at the beginning of the manga and turned 16 sometime before the magic mushroom story arc (this is somewhat supported by his saying he will lose a year if he eats a 17cm mushroom instead of a few months). Another possibility is that Genma and Ranma's mom being pretty traditional could use the old way of counting a child's age where at birth you were one and counted up at new years and not on the birthday meaning Ranma could be 14 or 15 by the modern way of counting age (though this is really unlikely but considering how Ranma's mom and Genma are; it is not as unlikely as it should be). For information on the old way of counting age see: Old Japan tips.