Which Spanish motorway connects Madrid to Barcelona?

The Spanish motorway connecting Madrid and Barcelona is the Autovía A-2.

Also called the Autovía del Nordeste, the A-2 follows the historic Madrid–Barcelona corridor and largely replaces the former N-II national road. Its route passes major cities including Guadalajara, Zaragoza, Lleida and Barcelona, crossing the interior of Spain from the capital toward Catalonia.

The road is about 504 kilometres long and forms part of European route E-90. It is often confused with the AP-2, a tolled motorway that covers parts of a broadly similar Madrid–Barcelona travel corridor. The A-3 instead links Madrid with Valencia, while the A-4 heads south toward Córdoba and Seville.

The A-2 is not simply a local Barcelona access road: its numbered route extends from Madrid to Barcelona, making it the canonical answer to this question.