Does giving a creature -1/-1 until end of turn kill it if its toughness becomes zero during the turn?

Whenever a creature's toughness is reduced to 0 or less by any effect — including a -1/-1 until end of turn effect — state-based actions immediately check for and apply the 'dies' condition. A creature with toughness 0 or less is put into its owner's graveyard as a state-based action. This does not wait for end of turn.

State-based actions (SBAs) are checked continuously by the game: before every player receives priority, the game checks all SBAs and applies any that are relevant (CR 704.3). This means the moment a creature's toughness hits 0, it is removed from the battlefield well before the end-of-turn step when the effect would otherwise expire.

The 'until end of turn' clause on the effect becomes irrelevant for that creature, because the creature is no longer on the battlefield when the cleanup step arrives. The effect simply has no object to expire from. The creature stays in the graveyard.

Concrete example: Your opponent controls a 1/1 Goblin token. You cast a spell that gives it -1/-1 until end of turn. Its toughness immediately becomes 0. Before anyone receives priority again, SBAs are checked (CR 704.3, 704.5f), the game sees a creature with toughness 0, and the Goblin is put into the graveyard. It does not return at end of turn.

Note: if the creature had a toughness-boosting ability or another simultaneous effect keeping it above 0, it would survive — but the -1/-1 alone on a 1/1 is lethal immediately and permanently.