UD Challenge for the Cup

2001-02 UD Challenge For The Cup #37
2001-02 UD Challenge For The Cup Century Man #CM10
2001-02 UD Challenge For The Cup Cornerstones #CR6
2001-02 UD Challenge For The Cup Jersey Autographs #FPPB
Three inserts are with the base : Century MAn (numbered to 100), Cornerstones (numbered to 250), and Jersey Autographs (numbered to 75).

UD Mask Collection

2001-02 UD Mask Collection #64
2001-02 UD Mask Collection Gold #64
Upper Deck Mask Collection has only a gold version of the base, numbered to 50 copies.

UD Playmakers

2001-02 UD Playmakers #45
UD Playmaker is (I think) a set from the Bobblehead Series, but I'm not sure.

UD Premier Collection

2001-02 UD Premier Collection #35
2001-02 UD Premier Collection Jersey Dual #DBA
2001-02 UD Premier Collection Jersey Dual #DBF
2001-02 UD Premier Collection Jersey Dual Black #DBA
2001-02 UD Premier Collection Jersey Dual Black #DBF
2001-02 UD Premier Collection Jersey #BBU
2001-02 UD Premier Collection Jersey Black #BBU
UD Premier is the first one I think to have serial numbered base cards. Bure appears alongside Maxim Afinogenov and Sergei Fedorov for the dual jersey (numbered to 100), which has also a black version (numbered to 50). He also featured alone (numbered to 300), and has a black version (numbered to 50).

UD Top Shelf

2001-02 UD Top Shelf #19
2001-02 UD Top Shelf #109
2001-02 UD Top Shelf Sticks #SPBU
2001-02 UD Top Shelf Sticks Gold #SPBU
2001-02 UD Top Shelf Sticks #BJF
Bure appaered two times because of the update set. Sticks (1 per 12), has also a gold version numbered to 50, and a triple version with Jagr and Fedorov.

Upper Deck 

2001-02 Upper Deck #73
2001-02 Upper Deck #180
2001-02 Upper Deck #230
2001-02 Upper Deck Exclusives #73
2001-02 Upper Deck Exclusives #180
2001-02 Upper Deck Exclusives #230
2001-02 Upper Deck Fantastic Finishers #FF1
2001-02 Upper Deck Franchise Cornerstones #FC2
2001-02 Upper Deck Leader of the Pack #LP6
2001-02 Upper Deck Shooting Stars #SS8
2001-02 Upper Deck Skilled Stars #SS4
2001-02 Upper Deck Tantalizing Tandems #T4
Three bases, three exclusives. The third one is numbered to 50 though, unlike the first two, who are numbered to 100. A couple of inserts are in the set : Fantastic Finishers (1 per 36), Franchise Cornerstones (1 per 24), Leader of the Pack (1 per 24), Shooting Stars (1 per 9), Skilled Stars (1 per 9), and Tandems (1 per 36).

Upper Deck Honor Roll

2001-02 Upper Deck Honor Roll #15
2001-02 Upper Deck Honor Roll #45
2001-02 Upper Deck Honor Roll Honor Society #HSBB
2001-02 Upper Deck Honor Roll Honor Society Gold  #HSBB
2001-02 Upper Deck Honor Roll Honor Pucks #PPB
2001-02 Upper Deck Honor Roll Honor Pucks Gold #PPB
2001-02 Upper Deck Honor Roll Sharp Skaters #SS4
Bure has two base cards in the set. Honor Society, with his brother, is numbered to 100. Beckett says that not all the gold parallel, numbered to 25, were verified. Pucks (numbered to 225), has also a gold variation, numbered to 100. Strangely, Sharp Skaters is a 1 per 40 packs inserts.

Upper Deck Ice

2001-02 Upper Deck Ice #20
That's it! LOL.

Upper Deck MVP

2001-02 Upper Deck MVP #78
2001-02 Upper Deck MVP Combo Game-Used Souvenirs #CPB
2001-02 Upper Deck MVP Combo Game-Used Souvenirs Gold #CPB
2001-02 Upper Deck MVP Talent #MT7
2001-02 Upper Deck MVP Valuable Commodities #VC2
Pretty basic stuff, except for the Game-Used Souvenir Combo (1 per 296 packs), which has a gold version numbered to 50. Talent is a 1 per 12 insert, while valuable commodities is inserted at a rate of 1 per 24 packs.

Upper Deck Victory

2001-02 Upper Deck Victory #151
2001-02 Upper Deck Victory #395
2001-02 Upper Deck Victory Gold #151
2001-02 Upper Deck Victory Gold #395
Nothing more to say there. Golds are 1 per 2 packs.

Upper Deck Vintage

2001-02 Upper Deck Vintage #106
2001-02 Upper Deck Vintage #112
2001-02 Upper Deck Vintage #113
2001-02 Upper Deck Vintage #261
2001-02 Upper Deck Vintage #264
Five cards, five bases...

Vanguard

2001-02 Vanguard #42
2001-02 Vanguard Blue #42
2001-02 Vanguard Premiere Date #42
2001-02 Vanguard Red #42
2001-02 Vanguard East Meets West #8
2001-02 Vanguard In Focus #6
2001-02 Vanguard Memorabilia #46
2001-02 Vanguard V-Team #15
Last but not least, Vanguard! Base card has four parallels : Blue (1 per 49 hobby and 25 retail, numbered to 89), Premiere Date (numbered to 83), Red (1 per 96 hobby and retail packs, numbered to 38), and a One-of-One. My red parallel is not numbered though, East meets West has a suprinsingly 1 per 97 packs rate, while the In focus has a whooping rate of 1 per 481 packs, plus they are numbered to 55 copies. Memorabilia is a net cord from the 2002 All-Stars Game with Brett Hull. It's numbered to 200 copies and is a 1 per 97 packs insert. V-Team was a retail exclusive.