Seven. The default "Maximum Hand Size" is seven. What this means is, at the end of your turn, if you have more than seven cards in your hand, you have to discard down to seven.
402.2. Each player has a maximum hand size, which is normally seven cards. A player may have any number of cards in his or her hand, but as part of his or her cleanup step, the player must discard excess cards down to the maximum hand size.
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Tyrant-Thanatos says... Accepted answer #1
Seven. The default "Maximum Hand Size" is seven. What this means is, at the end of your turn, if you have more than seven cards in your hand, you have to discard down to seven.
There are quite a few cards that modify hand size in some way or another. Locust Miser, Minamo Scrollkeeper, Spellbook, etc.
December 13, 2017 3:17 p.m. Edited.