Yes! They're called taxi's. The taxi drivers in every port know the ships tours by heart, so haggle away till your down to 25-30% of the cruise price. Good Luck.
At many Med ports it is perfectly feasible to take public transport to local attractions that don't include "shopping opportunities". With a bit of research on the web for bus and train timetables and judicious use of Google Earth you should find easier/cheaper ways to do excursions. Where exactly are you going and what do you want to see?
We are going to gibralta. rome. florence/pisa. barcelona. monte carlo/monaco. cartagena. probally not in that order. any advise would be most welcome. thanks.
Gibraltar - Either walk into town (15 min) and take the cable car to see the apes or take the taxi/minibus tours offered at the quay, 25 euros each, which take you round all the main sites; I think these are good value on a first visit.
Rome - You can get the train 5 minutes from the port exit, about 10 euros return, takes just over an hour each way. Get timetables from Trenitalia.
Florence/Pisa can also be done by train from Livorno station, take the #1 bus from Livorno bus station. Florence is a long way though and may involve a change of train at Pisa. Pisa is relatively easy; buy tickets to climb the tower online in advance (at least 16 days).
Barcelona - Take the port shuttles to town (1 euro) and then the open top hop on/off tour bus on a first visit, about 20-25 euros.
Villefranche(Monaco/Nice) - Train or #100 bus from main coast road, every 15 min, 1 euro each way, Monaco about 20 min away (East/right), Nice 10 min (West/left).
Haven't been to Cartagena, sorry. More detail in my review of Independence 15/7/08.
The critical thing is to make sure you leave enough time to get back to the ship as it will not wait for you if you are late and are on an independent trip but not a serious problem in Barcelona, Monaco or Gib as you are not terribly far from the ship.