As a biased NZ fan some of my favourites:
The 92/93 Aus v NZ (Aus win 3-2). Australia won the first two then NZ won games 3 and 4 with Crowe getting 91 in both wins. Jeff Wilson played a blinder in the 4th game and hit the winning runs. The series came down to Chris Pringle needing to hit a six off the last ball at Eden Park against Merv Hughes which was a bridge too far.
End of an era for NZ Cricket as Warren Lees was dumped at the end of the season and Crowe would soon relinquish the captaincy due to his knee problems.
India v NZ in 93/94 (2 all). NZ won the first game and Fleming got 90 on debut and Danny Morrison took a hat-trick. India came back and won games 2 and 3. I went to the game at Eden Park where Tendulkar hit 82 off 49 opening the batting which was an outrageous strike rate in that era. Probably the best innings I've seen live. NZ won the last game with Shane Thomson and the recalled Adam Parore putting on a big partnership.
England v NZ 1987/88 (2 all). The last time NZ wore the beige. Greatbatch took one of the great catches at 23.45.
NZ v South Africa 1998/99 (SA won 3-2). Dion Nash captained as Fleming was returning from injury. Klusener and Astle in career best form. Astle also took one of the great outfield catches in game 4 that SA won with 2 wickets to spare. I remember Chris Harris coming out to bat to Eye of the Tiger at Eden Park.
Aus v NZ 97/98 (2 all). Mark Priest got recalled at Eden Park, Llorne Howell got a half century and NZ pulled off an unlikely win to square the series. Aus won the first two games and Gilchrist looked unstoppable. Fleming and McMillan put on a big partnership to get up and win the 3rd ODI.