Of course, I use False Swipe on practically any Pokemon I want to catch. (In Diamond, I have a Sneasel whose sole purpose is to use that attack.) However, there are some cases in which it's not a good idea to use that move:
-Catching a non-Ice/Rock/Ground/Steel Pokemon in hail or a sandstorm. The weather will KO the Pokemon after False Swiping.
-Catching a Pokemon with a recoil damage move. If you False Swipe it and it uses Take Down or something, it'll KO itself.
-Catching a Pokemon with a self-KO or escape move. It's even a bit risky to put it to sleep and switch out, because you never know when it'll wake up.
-After poisoning or burning the Pokemon.
For Selfdestructers like Graveler, I wear the Pokemon down with my Golduck (she has Damp) and then try to catch it.
Fortunately, most recoil moves wild Pokemon know are Normal or Fighting-type (a Machoke usually knows Submission), so for them, I False Swipe, hope that the Pokemon doesn't use the recoil move right afterward, then switch to a ghost Pokemon (especially my Gengar or Spiritomb, who can put the Pokemon to sleep).
Usually, when I want to catch a Pokemon, I bring along my special False Swiping Sneasel, and someone with a status-inducing move (especially paralysis for some of the more difficult Pokemon, since the status doesn't go away; or sleep, for someone with strong or self-destructive attacks). If I want a specific gender, I bring along someone of the opposite gender with Cute Charm--especially my male Lopunny (I was able to get all female Great Marsh exclusives by having him first in my party). I also bring him along if I plan to catch a ghost, since he knows Foresight.
Another alternative to False Swipe is Super Fang, which can't KO because it just cuts the target's remaining HP in half. This move is especially useful against a Rock or Steel Pokemon or something with high Defense, which would make False Swiping painfully slow. (unless you have a Scizor with Swords Dance or something). I bring along my trusty Pachirisu for this job, because she has good defenses and also knows Charm, which makes it less likely for recoil-move-users and herself to be KOed.
I came up with a reliable (though a bit time-consuming) method of catching wanderers like Mesprit and Cresselia. What made catching Mesprit time-consuming for me was finding it again after it fled--but fortunately I had my Staravia to fly me from place to place, and of course my trusty Marking Map. In each encounter, I did the following:
1. Pachirisu used Super Fang.
2. Pachirisu used Super Fang again. (I did this because False Swipe doesn't do a lot of damage and there's no time for a Swords Dance, and trying to put Mesprit to sleep is a bit risky. Super Fang can't accidentally KO with a critical hit.)
3. Sneasel used False Swipe. (I actually had to do this a couple of times to make sure Mesprit's HP was as low as possible.)
4. Raichu used Thunder Wave.
After that, I saved the game, found Mesprit again, and threw a Quick Ball. If it failed, I restarted the game, so as to preserve balls. Catching a legendary with only one ball is pretty sweet, don't you think? (Not like the twenty Ultra Balls I had to waste on Azelf...)
I think the most unnerving part of catching Pokemon is trying to catch a shiny. When encountering a random shiny in the wild, I'm unprepared, often times having none of my "catching Pokemon" in my party. There, I have to hope for the best by throwing balls and using status-inducing moves if my Pokemon have any. I never use an ordinary damaging move unless it's really weak--I learned that lesson the hard way when my Seadra KO'd a shiny Tangela with a critical-hit Twister. Also it's frustrating to try to catch a shiny with a self-damaging move. Today, for example, I encountered a shiny Geodude. Immediately I thought, "Oh no, what if it uses Selfdestruct?!" And I had no Pokemon with Damp. I had to cross my fingers and throw a Quick Ball in that situation...
The Seadra in the above example is the reason for what I think is the most frustrating thing about catching Pokemon: CRITICAL HITS!!! Too often I have accidentally KO'd a Pokemon with a critical hit, when I was too lazy or spontaneous to bring out my False Swiper. I really wish there was an item or something that can prevent them... or that Lucky Chant worked on the user.
