There were a reasonable number of VHS releases over the years but the selection was a bit hit and miss; not a lot of dramas but a fair few sports and documentaries. Your best bet to track any of these down is to search the online auction sites.

 If you have any details or cover scans for ones I'm missing please add a comment.

From a fellow collector:

Title
African Journey (1990)
All Heart (1997)
An Evening with Sir Howard Morrison (1990)
Back of the Y Masterpiece Television (2001-2)
Before the Mast (2000)
Billy T James Show (1981-84)
Blood, Sweat and Touring (1990)
Boy from Andromeda, the (1991)
Bumble (?)
Captain's Log (2001-2)
Cinema of Unease (1995)
Dress Up Box, the (2001-2005ish)
Epitaph (2001)
Fire-Raiser, the (1986)
Good, the Bad and the Rugby (1989)
Grasscutter, the (1988)
Hairy Maclary (1996)
Haunting of Barney Palmer, The (1987)
Heart of the High Country (1986)
Heartland (1992 - 96)
Hercules: The Legendary Journeys (1995 - 99)
Ihaka: Blunt Instrument (2000)
Lawless (1999-2001)
Letter to Blanchy (1996)
Magical World of Margaret Mahy, the (1994)
Mark II (1986)
Moko Toa (1998, 2000)
Mortimer's Patch (1980-84)
Mud and Glory (1990?)
Nearly No Christmas (1982)
New Zealand Wars, the (1999)
No Latitude for Error (1994)
Nutcase (1980)
One World of Sport (1991-?)
Oscar and Friends (1996)
Party Animals, The (2003 - 2004)
Popstars (1999)
Rainbow Warrior Conspiracy, The (1988)
Ray Bradbury Theatre, The (1991-97)
Rogue Stallion, the (1990)
Rugged Gold (1994)
Sam McGredy's World of Roses (1998)
Savage Play (1994)
Shaky Beginnings: The Shaping of New Zealand (2007)
Shipwreck (2000)
Shortland Street (1992-Now)
Sinking of the Rainbow Warrior, the (1993)
Skycrane (1983-84)
Son of a Gunn Show (1992-95)
Sound and the Silence, the (1993)
Steel Riders (1987)
Suzy's World (1999-2003)
Tommyknockers, the (1993)
Town and Around (1965-70)
Typhon's People (1993)
Wild South (1981-97)
World at Your Feet (1988)
Worzel Gummidge Down Under (1986-87)
Xena: Warrior Princess (1995-2002)
You and Me (1992-1999)
Young Hercules (1998-99)