I have mixed feelings about this. It depends on who you are correcting.
My GF, for instance, didn't appreciate it and she made a point to tell me that before we even started getting heavily involved because an ex of hers was really bad about it and it made her feel stupid. She is probably one of the worse spellers I've ever met and all her family is as well.
She and her mom are/were both factory workers for 20 to 40+ years and there is no need for them to worry about that stuff. I really don't care though, I am not with her for her spelling ability. (Plus I feel like I'm helping when she asks me to spell something for her)
However, she now asks me why things are spelled certain ways and the easiest way to remember how to spell the most common errors people make like "Their, They're, there" "its and it's" "You're Your" and so on. She has a better handle on that now.
As for spelling more difficult words, that I can understand for the majority of people... Words like definitely, accommodate, restaurant,
separate and so on are just silly spelled words. All those I still have trouble with myself! Restaurant is my least favorite word to have to write or type, I typically substitute it with "diner" hah! 
I think people correct others out of some sort of OCD thing or something like that. They just can't help themselves. It's not right and I feel embarrassed for the correcter rather than the corrected when I see it in public.
One last "However".... I really can't stand how some people intentionally misspell simple words. I'm not talking about making your texts shorter...I mean just completely and intentionally misspelling words to look cool. That drives me insane.....
My reply to those that speak dumb are "Let me get out my secret decoder ring to figure out what the heck you're saying!" (But only to my close friends, of course).
-Adriana