The open top Red Bus around the villages - Red Bus to Famagusta for the day. Jeep Safari to the Troodos. All the boat trips.

I second the red bus trip village but would advise that you book the trip and finalise the pick up details in person. When I booked the Famagusta trip over the phone after doing the village trip I was given a pick up point and time which was totally different to where the bus turned up and we missed the trip

Yorkiebrum

to directly answer your question there are two main tour operators on in the south , most places selling trips will be acting as an agent for one or the other, i have found both fairly equal in what they do and on price, to see whats available please read my what to do where to go thread near the top of the cyprus index page

yasus
wizard

We found the Red bus and planned to just get on at the start of the tour -- but plans change -- next time

The Boat trips are mostly all good - - if you like fishing watch the boats arrive in harbour at the Golden Coast and find which is catching before booking - Oh Yes remember it's a 5am start from the Harbour

Stephanie did the Jeep safari off road with Mike as her driver (apparently a lot of returning passengers ask for him) he asked on or off road and when he went off road there really was no road to follow Stephanie came back absolutely thrilled with her day

Diving LOTS of trips diving tons of choice of dive shops and schools if you don't dive at least do a Discover Scuba Diving trip (DSD) I did my PADI Advanced qualification there and enjoyed water warmer than in Sharm El Sheikh or the Carribean as well as English instructors and Cypriot instructors who you could think were actually English such is the local culture
If you are suitably qualified (min Advanced Open Water) there is the site site of the wreck of the MS Zenobia which is classed as the #3 wreck dive site in the world