Ceuta is one of two Spanish exclaves in North Africa (the other one being Melilla. The territory had several rulers before the Portuguese in 1415 took control of this city east of Tangier. Since 1580 it has been under Spanish administration but has the status of an autonomous city despite being located on the African continent almost directly south of the autonomous city of Gibraltar.
This exclave was in the spotlight in 2005 together with Melilla because hundreds of people were trying to climb over the border fence. Ceuta being part of Spain and therefore a safe haven for Africans made it a prime target for migrants. Today the border is heavily protected by the Guardia Civil. The European Union invested a lot of money to make illegal immigration more difficult.
Ceuta is easily accessible from Algeciras (Cádiz) by ferry. High speed ferry services run between Ceuta and mainland Spain every half hour as of summer 2007. One company operating the route is Trasmediterranea and in the winter season they have three daily departures as of December 2013. Cruise ships occasionally visit, and usually dock within a few blocks of the easily-walked town.
Cruise ships do visit, but only very occasionally.
By land, Ceuta is only accessible from Morocco. If arriving by bus, you may have to take the bus to a nearby town and then a grand taxi to the border. For example, coming from the south, the closest an intercity bus will take you is to Fnideq. From there, take a grand taxi to the border (4 dh). It is much easier to go to Ceuta from Tetouán than from Tangier, as most buses from Tangier go through Tetouan anyways before heading north to Fnideq.
You will need a passport to cross the border with Morocco in either direction and official ID to book passage between mainland Spain and Ceuta. Rules for immigration are the same as for Spain. Ferry ticket salesmen have been known to sell tickets without requiring the proper identification, but security at the port going from Ceuta back to Algeciras can be much more strict. Spanish citizens need only their national ID cards, or DNI, but foreigners will require their passports to return. Just because you are not leaving the country of Spain doesn't mean you shouldn't carry your passport.
The increased border security may result in minor waiting time. This could be longer if you travel in summer when the main holiday season in Spain and France starts and lots of families return to their homes in Morocco. Note that there seem to be separate lines for Moroccans and foreigners at many border crossings, ports, and security checks. If you find yourself stuck in an extremely slow moving line and do not look Moroccan, try getting noticed by an officer. You may find yourself ushered past the line and processed very quickly.
Ceuta is a tiny city. Best way is by bike or on foot. The area near the waterfront and shopping area is nicely landscaped and attractive considering the heavy traffic supported.
There are taxis available. Make sure they use the meter or negotiate a price before you get in. There is a decent bus service with modern and spacious buses running around the city with stops at the border with Morocco. Look for a bus marked "Frontera".
The area hosts a few churches, and fortifications for those interested in Euro-African history and governmental relations. The downtown area and waterfront is remarkably clean and attractive with safe walking, and offers many stores and cafés serving the shoppers noted earlier.
There is a semi interesting fort in town with some views. There is also a lighthouse to see. Other than that are lovely beaches and desert areas to explore.
Ceuta is no longer a free port. The city was a free port before Spain joined the European Union in 1986; now it has a low-tax system. You will see that the economy of this city focus on people transiting to/from Morocco and one-day shopping tourists. Offerings range from footpath hawkers and kiosks, to modest stores (with goods you'd expect from the types of visitors noted above), to fine jewellers and an El Corte Ingles department store.
Offerings range from pavement cafés and a drive-in McDonalds to a few fine restaurants.
Ceuta is a great city to go out. There are several pubs and clubs and a great tapas route.