Both have regular connections to Europe, the Middle East, Africa and Asia. Flights tend to be quite expensive.
Trains go from Aleppo to Istanbul and from Damascus to Amman.
Service taxis also run from Damascus to most of the neighbouring countries. You can bring your own vehicle into Syria, but you will need a carnet de passage and local third-party insurance. In summer, the ferry also stops in Cyprus. There are internal flights between Damascus and Aleppo, Qamishle, Lattakia and Deir ez-Zur. Syria's road network is excellent, and buses are frequent and cheap - most Syrians use the bus, as very few have their own car.