We usually use the 'time-reset' method with a straight 31 IV male Gyarados and a straight 0 IV female HA foreign Gyarados and run multiple projects so that almost every egg counts.
We have streamlined the process to the point that we can generate almost perfect Pokemon from a blank state (0 perfect IVs) in barely more than half an hour and we still have alternate methods to fall back in the case we need flawless IVs and/or rare sexes. That is our way to deal with it - German efficiency, we think.
While breeding dozens of eggs, when I get too tired, I just briefly rest (eyes closed, while still holding down the circle pad to the left or right), this is during the time where I just listen to the in-game route/city music while cycling back and forth past the daycare center, and when I hear that the music doesn't change any more after holding the circle pad in the appropriate direction for too long (I press 'A', and sure enough, it's time for the egg to hatch). I also look forward to getting random lv3 hatchpower while I keep my profile status set to "hatchpower pls" xD, I thank random passersby and friends for that.
I usually breed either when I have something to do as well. I also enjoy breeding while riding the train. It feels kind of therapeutic to just go all zen and breed. It is just relaxing...especially when I'm all worried about everything else in my life...
Same as everyone else, watching TV/movies/streams helps pass the time. Also, the knowledge I have more than enough BP to buy lots of Ability Capsules, so I don't need to worry when my 6IV Banette has the wrong ability ~_~
Same. I also find that doing it in short bursts helps. I usually do ~10-20 eggs and if I don't get what I am looking for I either switch what I am breeding to curb frustration or stop for a while and try again later.
The problem with this thread is that it assumes the posters are still sane :P
Seriously, though, I got over the monotony by having breeding races with my friends. We pick the Pokemon we each want, and the first person to get one with 6IVs, correct egg moves, and a good nature wins. Adding a competitive element makes it go much faster; plus, it feels really good when you win.
I keep sane when breeding my making it more involved, and a challenge.
For example, if I wanted to get a 5iv Relaxed Aron, I'd breed any random Aron I had, giving it the Destiny Knot to hold, and giving a Power item to the 6iv Japanese Ditto I permanently keep in the Day-Care. Then, I keep breeding until I have a Relaxed Aron, which will have at least 3ivs.
Then, I give it the Everstone, the Ditto a Destiny Knot, and keep breeding. When I eventually obtain a 4iv Aron (which doesn't take that long), I substitute it for the 3iv Aron, and continue breeding. With this method, it doesn't take too long to get a 5iv Pokemon.
The other advantaged with this is that because the Ditto is Japanese, I can breed for a shiny and a 5iv Pokemon at the same time. This saves a lot of time.
To be honest, I'm pretty sure all of my competitive Pokemon are only 3-4 IV because I am the most impatient person you will ever meet. Except for the 5IV Skarmory and Azumarill I got off wonder trade
It helps that I got a flawless Japanese ditto from someone on a trade forum a while back. That makes it easy to get the stats. Of course, that ditto was not acquired through normal gameplay, so I guess I'm cheating a little...But I'm not using said ditto for anything other than eggs.
It does get very tedious when I watch the screen the whole time. I just hatch the eggs five at a time, while watching a movie or listening to music, or even while drawing with one hand and pressing the 3DS's d-pad with the other.
It totally is sometimes. It's relaxing because you don't have to do much besides move back and forth. Half of the time, I need to be looking at something other than the 3DS screen to keep from getting sleepy, though.
Wait - I'm supposed to remain sane breeding tons of Chimchar, Torchic, and now Froakie for IV breeding?! Wish I knew that sooner!
I took a break breeding Chimchars (trying to get Adamant or Jolly when neither of the ones I'm breeding have them...) and now I'm working on getting a Froakie to work up like what showed up in the Greninja episode of The Dex. Luckily, I've got a few with Protean, and one with perfect everything but HP and Sp. Attack, albeit that one has Torrent. I pick up the egg, deposit it immediately, repeat until I have four, then switch out everyone for the eggs except Flame Body Talonflame and Blaziken. The only reason it's not five eggs and I keep the Speed Boosting chicken on the team is...my Talonflame no longer carries a transmittable form of Pokerus while Blaziken still does. And I still need to give it good moves. (hint: Double Kick, Slash, Bulk Up, and Blaze Kick don't count as really good) Doing all this while kicking NPC butt in the nearby Battle Chateau or watching YouTube videos helps keep me from losing what's left of my mind.
I have horrible shiny luck.
My advice for keeping sane/motivated:
-Don't count, it only makes it more aggravating. I check how many eggs I've hatched before I start MMing by battling a friend, and after I hatch the pokemon I check how many eggs it took by doing the same thing.
-When you're sick of hatching eggs, take a brief break and go EV train some other pokemon with hoard battles, grow berries, challenge the battle maison, whatever. Then return to hatching.
-Watch videos of other people hatching the pokemon I want and be like "doooood that's awesome, alright I can do this!"
-Don't attempt to hatch so many eggs in a short time. I obsessively hatched 1200 eggs in 3 days and it drove me batty.
-Don't expect to get a shiny anytime soon, remember that it's all up to odds.