I learned Spanish from a native English speaker.
And Mrs Iggy’s English teachers have been native Spanish speakers.
I learned decent Spanish grammar. Unfortunately some of her teachers have not been quite so good with grammar and enunciation.
I teach languages of which I am not a native speaker. One could argue about the relevance of pronouncing dead languages like Latin, but the students need to be able to understand both me and next year’s teacher when we say the word. In that case, I just concentrate on the things that impede communication. They can’t be convinced to roll Rs, for instance (nor can most of my colleagues who teach Latin).
For the modern languages, again, I correct the worst offenses, but I warn them that I might lead them wrong in either pronunciation or usage, and to pay attention to the native speakers and follow them. I try to get native speakers to attend classes, and tell the students to follow the accent of the people who grew up in that country.
There’s one basic sound that I apparently mispronounce. I don’t know what’s wrong with it, but I’ve tested and multiple people have independently caught me making the mistake, so… better they learn to speak the language with an error than not learn to speak it.
For both languages I learned at school (English and French - I was on the maths/science track) all teachers were Germans* - that’s almost invariably so in Germany because teacher training and employment is structured as a lifetime job, you have to have studied two subjects as a teacher and there is very little overlap between the languages natively spoken by the 2nd generation immigrant population (Turkish, Russian, Arabic, Italian, Greek, …) and the main foreign languages taught at school (English, French, Spanish, …).
The teachers were well qualified and usually had spent part of their studies abroad. One major resulty was that the only accents that we were exposed to were RP and standard French, respectively, i.e. we were ill prepared to understand e.g. US English.
- once or twice we got exchange teachers from the UK and France for half a year or so but they assisted the main teacher who retained responsibility over lessons and grading.
My high school French teacher was an American, but she taught pronunciation so well that I was taken for French by French speakers (and by a group of Germans, but I think that was because of my hat) when I finally visited.
My high school Latin teacher was a non-native speaker.
Mine, too. 
Actually, I learned Latin from three different teachers. My first-year teacher had a very thick East Texas accent, my second-year had a South African accent, and my third-year had a Michigan (Midwestern) accent. You can tell which year I learned what by the accent I use when I say it.
I took four years of Russian in high school from an American, but I believe she had a very good accent (bless you, wherever you are, Anna Morrisovna). I was going to continue with Russian in college, but my first college taught languages very badly so I quit. At a later college, I wanted to take up something completely different so I started learning Japanese, from a native speaker (Taguchi-sensei). Then I spent a year at school in Japan, where I was on the other foot - I was teaching (under the table, for cash) American pronunciation of English to Japanese people. Some adults, and some high school and jr high school students. They already had learned the grammar and vocabulary, so all they really needed was to practice pronunciation. Some of the high school students were very good, although they still had slight accents they pronounced all their L’s, R’s and Th’s correctly and naturally.
Anyway, I learned Russian from a non-native speaker, but I never had a chance to test my accent out. The closest I got were 2 Ukrainian students in my dorm at my first college who, I believe, were speaking Russian but who spoke it so fast that I couldn’t catch most of what they were saying. Or maybe they were speaking a Ukrainian dialect. It had been over a year since I had spoken any Russian, so I didn’t attempt to converse with them, being afraid of total failure.
My high school Spanish teacher was an American. My first college Spanish teacher was Cuban. However, Spanish-speaking kids from other countries complained that his accent was all wrong.
In high school, my German, Russian, French, and Spanish teachers were all non-natives, but knew their respective languages very well.
Two of my three Swedish teachers were native speakers; the third had lived in Sweden for some time.
My college and post-grad Russian teachers were a mix of American, Finnish, Czech, and Russian. While I spoke Russian fluently after four years of university-level study, I didn’t master the accent until I had studied in Moscow for six months. Russians usually take me for either a Bulgarian or a Balt.
My German was at one time better than my Russian, but I was never taken for a native speaker, and I was told I spoke Swedish with a Finnish accent.
No one ever identifies me as an American.
This Toshi she keeps talking about must be some really awesome dude! 
I learned French first in Quebec, then in West Africa. Does that count?
My German prof in college was not a native speaker, and he also taught Russian.
I studied Portuguese and Inuktitut under non-native speakers.
My high-school German teacher was not a native German speaker. At uni, I had both native and nonnative German speakers for my classes, but the nonnative ones really knew their stuff.
At University, I had a husband and wife team teaching mandarin Chinese. He was a native American speaker and a Harvard PhD in Chinese. Freakin’ awesome to explain the root meaning of words, grammar, common mistakes of foreigners, tones, etc. His wife, a native Chinese speaker, taught me how to speak. It was a great combo.
My college French teacher was Chinese.
My high school French teacher was terrible. There was a running joke in our class that she was only ever one lesson ahead of us. I was in my 20s before I learned about stuff as basic as direct object pronouns (E.g. Je le faire).
My college Spanish teacher was a native speaker, and although I learned a lot in just one year, she couldn’t explain grammar concepts very well (eg the difference between por and para) because they were so natural and obvious to her.