I have a 3YO (3 the end of March). He wasn't saying anything at 16 months. This is when I started to worry more. People will tell you not to worry, but they just don't understand. It's easier said than done. I still worry, but my worry is a tad gone since he has actually started saying words...after he turned 3! He had said mama at 6 months and then quit saying it at one point. Started saying it again, but it was mamama, and I don't think it was the name for me, he was just saying it. He now says mom, but he has to think about saying it, if that makes any sense. He says it by request. He has said some things once and never again. He walked at 15 months. He was a very cranky baby - he had colic. I don't know if colic had anything to do with his issues, but he was a cranky baby! At 18/19 months, we went to the doctor to talk about it. Dork never told us about the state being able to evaluate my child for free - or the university in our town that has a great program...but I found it out anyways. That's what you get for going to a new doctor in a town he just moved to! grrr....

At 22 months, I had my child evaluated at the university, who has a grad school program in Speech Therapy. (So if you have a university by you, check to see if they have a speech therapy grad program, and if they do, chances are they will give speech therapy services, possibly for very cheap - could depend on the university (I get it for $300/semester - (2) 45 minute sessions/week). A lot of insurance doesn't really cover speech therapy, and if they do, it could be only 20 sessions a YEAR! This is what my insurance covers).
My child did not point until he was 2 years, 3 months. He just in the past 4 months started nodding and shaking his head. His only words until he turned 3 were only general words. He would say a word once and never again. General words were "this, that, here, there, I do, what's this, what's that"
In the past few months he has started saying more words every week. He says a FEW 2-word sentences. It would be hard for others to understand a good amount of what he says, but they can also understand some of what he says.
If you didn't know my child didn't talk, you wouldn't know anything was wrong with him. He is so social and understands EVERYTHING.
The not pointing, shaking, nodding head, waving goodbye...these are all clues (in retrospect) that something was wrong. It's all clues to his puzzle. He gagged on his food twice a day until he was 16 months. That could be due to enlarged tonsils (we took him to an ENT (ear, nose, throat dr.) - to eliminate any physical problems, but I think it has something to do with his delay. He was fine, heard well, never had any ear infections, and only 2 vaccines. No more since he was 2 months.
The university thinks he has apraxia, but has advised I get a professional who works with that a lot to get an actual confirmed diagnosis. I have to travel to the big city for this a few hours away, so I haven't done that yet.
If your child isn't pointing, waving, shaking, nodding head, etc; make sure you get Occupational Therapy (OT) as well. I really think the OT helps immensely, and I only started it in January. I had a friend tell me to have him evaluated, but I didn't think he needed it. The university advised me to, so I did. They work to get the brain functions all working together by doing certain activities...by getting these brain functions to work together, this will eventually help your child speak...and do all the other things. Of course, depending on what may be wrong, will depend on what therapies will help him.
Boys are more likely than girls to have a speech delay.
Now, I have a 19-month old who worries my husband because she doesn't say many words...and some of what she says, she mimics my 3YO who doesn't talk right. *sigh* But she pointed at 10 months, she waves hello and goodbye, she nods and shakes her head, she can stick her tongue out if I do, she can mimic a new sign right away if I teach her one (Ryne took a few times to get it). She doesn't have the issues he had, so I'm not worried - well a little, but she will repeat the few words she says on request.
I know my post was a book, but I hope it helped you. Either it will make you worry more, or less...or confirm that your gut is right.
Good luck in your endeavor. You are welcome to PM me if you have any questions.