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there are no illegal cards, just banned cards. look for a list online.Most cards in Yu-Gi-Oh are legal. The only exceptions are those that are fan-made, counterfeit, or listed here:

They consist mostly of the 'Egyptian Gods', the 'Match Winners', and a few other strange or absurdly powerful cards.

Do not confuse 'Illegal' with 'Forbidden'. 'Illegal' cards can't be used at all, except in friendly matches where all parties agree that they can be used. Cards that are 'Forbidden' simply can't be used in 'Advanced Format' sanctioned play (in 'Traditional Format', they are 'Limited' - or one-per-deck - by default). Plus, the official banlist (list of cards with restrictions on them) is updated every March and September, so a card that was previously 'Forbidden' may be playable again when a new version of the banlist comes out.