I've gotten so many letters from my villagers that I have to constantly keep going back and clean out the ones that I shouldn't keep anymore.
I use one of the tabs for all the letters from Gulliver, your mom, Katie, and Nintendo. But when it comes to villager letters, I keep ones that are funny or really sweet.
I always keep the letters that villagers send when they move out. That way I can go back and remember who all was once living in my town. I also try and keep really nice letters villagers send me. They make me happy to see
I never keep Gulliver, Nintendo, or mom letters I don't see the need to.
I only keep the ones that are really sweet from my favorite villagers. Like the ones from Zell. He used to send me letters maybe every other day or two because I befriended him obsessively. As a smug, he sent me the most darling letters.
Now, Punchy sends me a letter just about every day that are super sweet and funny. Which is really odd since Hugh was my lazy villager from the beginning and I rarely got letters from him (he was my "best friend" since he hosted my birthday party, gave me a heart shaped cookie, gave me his picture). But I won't complain. Punchy is starting to really warm up to me.
I used to save letters from everyone that moved in other games as a kind of momento of them. Now I don't care as much, and on NL I don't have any letters saved. I might save one if one of my babies accidentally moves.
I keep the ones that make me smile, either because I find them funny or because they make me happy. I also keep the villager birthday letters as a reminder until the villager has their birthday.
I don't keep specific letters. My post office is full of letters for storage space and I have to admit I only recently started actually reading what they wrote
I save all the moving letters (and keep them in order in a separate tab), certain events and milestones that you only get 1 letter for (post office rewards etc) and birthdays. I have a few letters that I found really funny or sweet too, but since I have started getting repeats of some I now chuck a lot of them.