I adore this song and performance - it got remixed with a syrupy orchestra on it for the single but the film version with just the piano and multitracked vocals was perfect. I loved the film in my early teens as well, and it got me into Janis Joplin.
And sod it, might as well post this, I know it offends the 'real' Guns N Roses fans but there's nothing about this song or video I don't love.
I know this is an overplayed 80's pop song but due to circumstances it still resonates with me. In either late 84 or earlier 85, I was heading via car to NOLA back from a shipyard in Pascagoula MS. My job was a S%it show and the woman I was in love with or at least thought I was in love with broke up with me over the phone while I was at work and took her daughter and moved back to her ex husband. I was an emotional wreck. This came on the radio about half way home and I was in tears for the next 50 miles. When I hear this today, through the power of music, I'm almost transported back to that car trip.
I'm a sucker for great love songs myself. I don't know about "big" but here are some greats in my mind:
"Heroes" - David Bowie
"I Am A River" - Foo Fighters
"Home" - Foo Fighters
"Goldilox" - King's X
"Every Little Thing She Does Is Magic" - The Police
"Go to Bed Early" - Brad Paisley
"How Lucky Can A Man Get" - Gavin DeGraw
"In Your Eyes" - Peter Gabriel
"Lucky This Time" - Mr. Big
"My Naomi" - Paul Gilbert
"Mr. Spock" - Paul Gilbert
"Face To Call Home" - John Mayer
"Who You Love" - John Mayer
"My Life" - Saigon Kick
"One Sweet Love" - Sara Bareilles
"I Feel the Love Between Us" - Sara Groves
"Army Of One" - Coldplay
"Magic" - Coldplay