Does a spell with X in its mana cost have a mana value of 0 while on the stack?

When a spell with X in its mana cost is on the stack, X equals the value chosen by the player as they cast it. The mana value (formerly called converted mana cost) is calculated using that actual chosen value of X. This is the exception to the general rule about X.

The general rule (CR 202.3b) states that X is treated as 0 when calculating mana value except while the spell is on the stack. CR 202.3d clarifies that while a spell is on the stack, X equals the value chosen for it when the spell was cast.

For example, if you cast Fireball choosing X=5 and paying {5}{R}, its mana value on the stack is 6 (5 for X plus 1 for {R}). This matters for effects that care about the mana value of spells on the stack, such as a Counterbalance trigger or a spell that says 'counter target spell with mana value 6 or less.'

However, once the spell leaves the stack — if it resolves or goes to a graveyard — and the card is in any zone other than the stack, X is treated as 0 again. So Fireball in the graveyard has a mana value of 1 (just the {R}).

In summary: on the stack X = chosen value; everywhere else X = 0.