Thanks to Dennis for providing us with these Boy Meets World transcripts.

Jump to season: 1 - 2

Season 1

1x01 - Pilot
1x02 - On the Fence
1x03 - Father Knows Less
1x04 - Cory's Alternative Friends
1x05 - Killer Bees
1x06 - Boys II Mensa
1x07 - Grandma Was a Rolling Stone
1x08 - Teacher's Bet
1x09 - Class Pre-Union
1x10 - Santa's Little Helper
1x11 - The Father/Son Game
1x12 - Once in Love With Amy
1x13 - She Loves Me, She Loves Me Not
1x14 - The B-Team of Life
1x15 - Model Family
1x16 - Risky Business
1x17 - The Fugitive
1x18 - It's a Wonderful Night
1x19 - Kid Gloves
1x20 - The Play's the Thing
1x21 - Boy Meets Girl
1x22 - I Dream of Feeny

Season 2

2x01 - Back 2 School
2x02 - Pairing Off
2x03 - Notorious
2x04 - Me and Mr. Joad
2x05 - The Uninvited
2x06 - Who's Afraid of Cory Wolf?
2x07 - Wake Up, Little Cory
2x08 - Band on the Run
2x09 - Fear Strikes Out
2x10 - Sister Theresa
2x11 - The Beard
2x12 - Turnaround
2x13 - Cyrano
2x14 - I Am Not a Crook
2x15 - Breaking Up is Really, Really Hard to Do
2x16 - Danger Boy
2x17 - On the Air
2x18 - By Hook or By Crook
2x19 - Wrong Side of the Tracks
2x20 - Pop Quiz
2x21 - The Thrilla' in Phila'
2x22 - Career Day
2x23 - Home

Random Boy Meets World Trivia

Several times throughout the years they mention how Cory and Topanga first met, but it's never the same story. Their "first" meeting happened at several different ages and places.