DON'T DROP COMBOS. Don't drop grabs, regrabs, or punishes out of grab. Don't give your opponent free space (especially marth and falcon, in this case).
If you must, or plan to hit a shield with an aerial, always space aerials outside of grab range. Once you have enough control to space moves accurately you can bait grabs (must be very familiar with opponent's grab range)
Don't get caught in your shield often. Know which situations are safer than others when it comes to shield usage.
Oh and don't miss L-cancels.
That takes care of most things that cause grabs Imo (mostly mistakes). On to specifics?
Falcon- greatest DD in the game and you have to learn how to deal with it. Being able to react quickly is paramount. Grabs are always an option for falcon, his basic approaches lead to grabs, and he has reliable ABC combo's on Ganon out of dthrow/uthrow. You can't let his DD intimidate you into overuse of shield. It's better to know exactly what his options are, and react quickly to counter an approach when you think it's coming... in a way that does not give him free space OR an easy grab/punish (high ftilt, jab/cc jab, uair, etc). When I get hit I primarily DI down and away to try to get away from grabs and if I must tech, I will try to tech before falcon can set himself up for mindgames or multiple option coverage.
Marth- spacing or aerials is crucial and and centered around his grab range (not to mention his fair, but that's another story). His DD is almost as good as falcon's because of this and one grab from marth usually leads to a string of grabs or a short combo. If nothing else, Marth can always pressure Ganon following a throw. Keep him outside until you can space an aerial accurately or deal with one of his approaches properly. Mis-spaced approaches will give marth free grabs. Aside from DI'ing approaches away, if you get grabbed, you must DI his throws properly and tech as quickly and as intelligently as possible to prevent multiple regrabs (not to mention other punishes like fsmash).
Sheik- At least she doesn't have a DD, lol. Any time sheik is inside she can get a grab- out of jab, any tilt, or even l-canceled aerials. Then Ganon gets rekt. A strong ground game will make sheik jump more and get you punishes. If your ground game is weak you'll get grabbed a lot. Patience is really important and your approaches must be chosen wisely. DI those jabs and tilts away to prevent gimme grabs. I like to DI up and away, all the way to the ledge quite a bit. If you are very comfortable on the ledge while being pressured it is basically neutral game. Reseting the game to neutral is much better than eating a grab.
Boredom ramble.
OK I don't know how to get rid of that smiley. I give up