ждать

"ждать" can take either the Accusative or the Genitive, depending on how definite the thing being waited for is. The same alternation affects искать, просить and требовать.

Accusative — a definite, concrete or animate object.

• Я жду сестру. — I am waiting for my sister.
• Я жду автобус номер пять. — I am waiting for the number five bus.

Genitive — something abstract or indefinite.

• Мы ждём перемен. — We are waiting for change.
• Она ждала ответа. — She was waiting for an answer.

Sometimes the case changes the meaning:

• Я жду поезд. — I am waiting for the train. (a particular one, the 7:40)
• Я жду поезда. — I am waiting for a train. (whichever one comes)

Some combinations are normally Genitive whatever the context: "ждать своей очереди" (to wait one's turn), "ждать случая" (to wait for an opportunity), "ждать у моря погоды" (to wait for something that will never come).

In speech the distinction is blurring, and you will often hear the Accusative with concrete inanimate nouns ("ждать трамвай" rather than "ждать трамвая"); with abstract nouns the Genitive remains standard. Negation favors the Genitive for a separate reason ("Никто не ждал такого ответа"). The perfective подождать behaves the same way.