"Syndication" can refer to reruns of shows that originally aired on broadcast networks (or in other countries), something that's particularly common on PBS, as well as BBC America (and really, pretty much any cable network). But on this page I'm going to try to stick to shows that originally aired in syndication, and not on any particular network. This may get a bit tricky, but I'll do my best.

The New Adventures of Pinocchio (1960-1961)
The Alvin Show (10/4/1961 - 9/12/1962)
Tales of the Wizard of Oz (9/1/1961 - 12/?/1961)
The Mighty Hercules (9/1/1963 - 5/1/1966)
The Marvel Super Heroes (9/1/1966 - 12/1/1966)
Donahue (9/14/1970 - 9/13/1996)
New Zoo Revue (1/24/1972 - ?/?/1977)
Jeopardy! (1974-present)
The City That Forgot About Christmas (1974; special)
The Muppet Show (9/5/1976 - 5/23/1981; aired on ITV in the UK)
Family Feud (1977-present)
SFM Holiday Network (1978-91)
The People's Court (1981-93)
Entertainment Tonight (9/14/1981 - present)
Inspector Gadget (9/12/1983 - 2/1/1986)
G.I. Joe: A Real American Hero (9/12/1983 - 11/20/1986)
He-Man and the Masters of the Universe (9/5/1983 - 11/21/1985)
Star Search (9/?/1983 - 4/?/1995)
Wheel of Fortune (9/19/1983 - present)
Voltron (9/10/1984 - 11/18/1985)
The Transformers (9/17/1984 - 11/11/1987)
Super Sunday (10/6/1985 - 10/?/1986)
The Care Bears (9/14/1985 - 11/25/1988; also aired on ABC)
ThunderCats (1985-1989)
Throb (9/6/1986 - 5/21/1988)
Popples (1986-87)
Charles in Charge (1/3/1987 - 11/10/1990; s1 aired on CBS)
Captain Power and the Soldiers of the Future (9/1/1987 - 5/27/1988)
DuckTales (9/18/1987 - 11/28/1990)
Star Trek: The Next Generation (9/28/1987 - 5/23/1994)
Teenage Mutant Ninja Turtles (12/14/1987 - 3/29/1991; s4-s10 aired on CBS)
Live! (1988-present)
Darkwing Duck (9/8/1991 - 12/5/1992)
Swan's Crossing (6/29/1992 - 9/25/1992)
Beakman's World (9/19/1992 - 5/?/1993; also aired on TLC; s2-s4 aired on CBS)
Star Trek: Deep Space Nine (1/3/1993 - 6/2/1999)
Bill Nye the Science Guy (9/10/1993 - 6/20/1998)
Space Precinct (1994-95; originally on Sky One in the UK)
Gargoyles (10/24/1994 - 5/15/1996; final season aired on ABC)
Hercules: The Legendary Journeys (1/16/1995 - 11/22/1999)
Night Stand with Dick Dietrick (1995-99; also aired on E!)
Xena: Warrior Princess (9/4/1995 - 6/18/2001)
Honey, I Shrunk the Kids: The TV Show (9/27/1997 - 5/20/2000)
Earth: Final Conflict (10/6/1997 - 5/20/2002)
Jack of All Trades (1/22/2000 - 12/2/2000)
Andromeda (10/2/2000 - 5/17/2004; s5 aired on Sci Fi; originally aired on Global in Canada)
Starhunter (11/1/2000 - 4/1/2004; originally aired on The Movie Network in Canada)
Mutant X (10/6/2001 - 5/17/2004)
She Spies (7/20/2002 - 5/17/2004)