For the sake of the answer, we'll consider a hypothetical format where all cards since the beginning of the PTCG are usable. This is because plenty of cards referenced cannot be used in official formats, as none allow for the use of Ruby/Sapphire, Diamond/Pearl, and X/Y sets in correlation with one another. I also won't be including any images, but instead the Bulbapedia article for the following card.
In addition, a big thanks to Staka~ for answering my question here, as then it'd have taken me far longer to research if this is even possible at all. Alright, time to get on with it, shall we?
Pokemon Cards with the MOST Attacks
Sorry, I was wrong, there are over 100 moves a single card may use.
Essentially, the use of the card Marshadow-GX (Burning Shadows 80) has an ability that allows it to use the moves of any basic Pokemon in the discard pile. As there's no limit to how many basic Pokemon cards you can have in a deck. Just use several unique basic cards and viola!
Despite that, you can't exactly discard that many cards by having your opponent knock them all out, thus requiring the use of Dark Marowak (EX Team Rocket Returns 7) and its move Hard Bone. This allows you to discard dozens of basic cards without allowing for your opponent to collect all their prize cards! As long as your opponent can live through the attacks, likely through a bulky Pokemon card in play and several other benched Pokemon, stadiums cards, and various other things of the like that either reduce the damage taken or heal it off.
So in theory, you can discard a total of 53 Basic Pokemon cards, as you'd otherwise need the Marshadow, Marowak, the three energy cards necessary to use the move, along with one card in your deck and one of your prize cards not drawn yet, as for neither you and your opponent to lose the game; possibly 5 fewer in order to actually use all the moves that are usable by your Marshadow. Assuming that all your discarded cards have two different moves, including the two moves Marshadow has itself, you'd be able to get 98-108 moves on a single Pokemon, possibly even more if you can think up basic Pokemon with more than two moves.
Originally:
Long story short, it's 6 attacks
How? Well, by applying a Lv. X card to a traditional Pokemon card, then using a BREAK card on the same card, we are able to get a Pokemon card normally with 3 moves to 5 moves, at least in theory. There are two Pokemon I know of that this applies too:
- Raichu (Stormfront 8) <- Raichu Lv. X (Stormfront 99) <- Raichu BREAK (BREAKthrough 50)
- Machamp (Stormfront 20) <- Machamp Lv. X (Stormfront 98) <- Machamp BREAK (Evolutions 60)
The thing is, I'm not entirely sure if this is possible, as the Pokemon BREAK may only inherit the Lv. X card's attacks, rather than from both cards. As this can't be tested, due to Lv. X and BREAK cards being split across generations, and I have yet to find a source of some madman replicating this, I can't say which is true for sure. Regardless, we're going to move on as if both card pairing are able to use a combination of 5 moves total.
Also, you might've noticed I said the Pokemon Cards with the most attacks add up to 6 attacks. Well, that wasn't a typo, and that's all due to our good friend Ditto, more specifically, Ditto (XY Promo 40). With the use of its ability Metamorphosis Gene, Ditto is able to copy all attacks from an opponents Pokemon. Combined with its attack Stick On, Ditto can, in theory, inherit the moves of an opponents Lv. X BREAK Raichu/Machamp, and obtain 6 attacks.