there is a vice governer
BOB
When a Senator resigns and there is no pending election at the time, the Governor of the state picks a replacement
A special election can be held or the governor can appoint someone to the office. They serve what is left of the term.
They get another governor.
The lieutenant governor will step in.
The Lieutenant Governor take over.
The Leiutenant Governor
The Lt. Governor replaces the Govenor
If the governor of Texas dies, resigns, or is removed, the lieutenant governor will take his place until reelection.
The Governor
The Secretary of State assumes the power of the Governor when the current Governor dies, resigns, or leaves office for other reasons. The current Secretary of State in Arizona is Jan Brewer, a Republican. The current Governor of Arizona is Janet Napolitano, a Democrat, who is currently being considered to become part of President-Elect Obama's cabinet.
The Secretary of State. Arizona doesn't have a Lt. Governor but the constitution delegates this duty to the Secretary of State (along with the normal operation of that office).
After Alaska Governor Sarah Palin resigns (expected sometime in July '09), power will be transferred to Lt. Governor Sean Parnell, who will be sworn in during the upcoming governor's picnic in Fairbanks.