My oldest didn't talk until he was 22 months. And it turned out that he's advanced, which we weren't paying attention to due to his lack of speech. I'm not saying that late talkers are all advanced in other areas. But in my son's case, people assumed that he wasn't as smart because he didn't speak, and it turned out that he's very advanced, particularly in visual-spatial areas. I hate the assumption that speech is linked to intelligence.
With my son, up until 22 months, he said, "Dad", "dissie" (nursie), and "dissis?" (this is?). He knew a few signs, but I had been somewhat lazy about introducing them. He had fantastic receptive speech, i.e. he could understand and follow directions, point to a variety of requested objects in books, etc. He made his needs known through lots of grunting and pointing. He made a lot of eye contact and sometimes would animatedly babble to other people, which always sounded like, "Da da da DAda DA da dada DA". He didn't even say, "Mama".
One day, when he was 22 months, I gave him some water and he said, "Tay-too....". And he said, "wa-bwa", which was "water". That incident seemed to open the flood-gates for him. He started repeating any word we'd offer to him. He started using words to communicate what he wanted (e.g. "shoo?" /shoes for going outside). Within 3 months of this, he basically sounded like any other boy his age. And at some point, he spoke very well (by 3 maybe). He just turned 4 and he has great speech. He creates long sentences, uses big words and just manages to express himself well. People easily understand what he is saying and he is very chatty with adults.
Our ped really pushed for an evaluation, but we opted to skip it. DS was only 15 months at the time and we felt he just was operating on his own timetable. I read an insane amount of material on late speech, autism, hyperlexia (he knew all the letter sounds), everything you could name, and I worried myself a fair bit. I had read that most kids have a jump in speech around 18 months and around 24 months. So we decided to wait until age 2 to give him a chance to develop on his own. It seems like most people do the eval and intervention these days, but based on our gut feeling and what we observed with ds, we decided to wait and see instead.
You asked for anecdotes. I hope this helps in some way.