There were actually two series of RENAISSANCE-class ships. The first series, ONE through FOUR, were built in 1989 and 1990 at Cantieri Navale Ferrari at La Spezia. The second series, FIVE through EIGHT, of an improved design, were built in 1991 and 1992 at Nuovi Cantieri Apuania at Carrara. The second series of ships were slightly larger and carried 14 more passengers (114 as opposed to 100 on the earlier ships).

Now, as to where they are now.

RENAISSANCE ONE and TWO were chartered in the mid 1990s to a Singaporean firm who licensed the Renaissance name and logo. In 1998, a Malaysian company, Universal Cruises, bought the ships and renamed them THE MERCURY and THE NEPTUNE respectively. Universal later went under and both ships spent several years laid-up.

Eventually, RENAISSANCE ONE was sold to New Century Cruise Line and is now a floating casino in international waters off Singapore called LEISURE WORLD 1.

RENAISSANCE TWO was sold to EasyCruise and is now EASYCRUISE ONE.

RENAISSANCE THREE was sold in 1997 and renamed GALAPAGOS EXPLORER II. She has been running cruises in the Galapagos ever since.

RENAISSANCE FOUR was also sold in 1997, to the Haji-Ioannou family, who renamed her CLELIA II and use her as a yacht and also charter her as a cruise ship. (Stelios Haji-Ioannou is the owner of EasyGroup, though I think it is a coincidence that his first cruise ship is a sister of his family's yacht.)

RENAISSANCE FIVE and SIX were sold in 1997 to Sun Cruises, then a new company in Singapore started by former Star Cruises executives. They were renamed SUN VIVA and SUN VIVA II respectively. In 2000 Star Cruises bought Sun Cruises and renamed the ships MEGASTAR SAGITTARIUS and MEGASTAR CAPRICORN respectively.

In 2000, MEGASTAR CAPRICORN (RENAISSANCE SIX) was sold to Hebridean Island Cruises. She is now their HEBRIDEAN SPIRIT.

In 2001, MEGASTAR SAGITTARIUS was sold to Cruise West. She is now their SPIRIT OF OCEANUS.

Renaissance retained RENAISSANCE SEVEN and EIGHT through to the end, having disposed of the other six ships in 1997 as they prepared to take on the new R-class ships.

After they went under in 2001, the two ships were laid up at Marseille and renamed RENAI I and RENAI II respectively. They were sold in 2003 to Mauritius Island Cruises and renamed SUN and SKY respectively, becoming ISLAND SUN and ISLAND SKY in 2004. While both ships were initially to operate cruises in Mauritius, in 2004 they were both chartered to various travel agencies etc. instead. ISLAND SKY (RENAISSANCE EIGHT) is now chartered to Noble Caledonia while ISLAND SUN (RENAISSANCE SEVEN) has been chartered to Travel Dynamics International and renamed CORINITHIAN II.

So, to recap:
RENAISSANCE ONE -> LEISURE WORLD 1 (New Century Cruise Line)
RENAISSANCE TWO -> EASYCRUISE ONE (EasyCruise)
RENAISSANCE THREE -> GALAPAGOS EXPLORER II (Canodros)
RENAISSANCE FOUR -> CLELIA II (Haji-Ioannou Family)
RENAISSANCE FIVE -> SPIRIT OF OCEANUS (Cruise West)
RENAISSANCE SIX -> HEBRIDEAN SPIRIT (Hebridean Cruises)
RENAISSANCE SEVEN -> CORINTHIAN II (Travel Dynamics International)
RENAISSANCE EIGHT -> ISLAND SKY (Mauritius Island Cruises/Noble Caledonia)

Hope that helps.