Here is a working list of songs that hit #1 yet had lengthy stays at the #2 spot (before and/or after hitting #1). If you know of any others, please post them here.
Whitney Houston - "Exhale (Shoop Shoop)" 11 weeks at #2 1 week at #1
Coolio - "Gangsta's Paradise" 9 weeks at #2 3 weeks at #1
Mariah Carey - "Always Be My Baby" 9 weeks at #2 2 weeks at #1
Lady Gaga - "Poker Face" 9 weeks at #2 1 week at #1
Macklemore & Ryan Lewis f/ Wanz - "Thrift Shop" 8 weeks at #2 6 weeks at #1
LMFAO - "Sexy & I Know It" 8 weeks at #2 2 weeks at #1
Katy Perry - "Roar" 8 weeks at #2 2 weeks at #1
OutKast f/ Sleepy Brown - "The Way You Move" 8 weeks at #2 1 week at #1
T.I. - "Whatever You Like" 6 weeks at #2 7 weeks at #1
Daniel Powter - "Bad Day" 6 weeks at #2 5 weeks at #1
Gwen Stefani - "Hollaback Girl" 6 weeks at #2 4 weeks at #1
Leona Lewis - "Bleeding Love" 6 weeks at #2 4 weeks at #1
Beyoncé - "Single Ladies (Put a Ring On It)" 6 weeks at #2 4 weeks at #1
Pitbull f/ Ke$ha - "Timber" 5 weeks at #2 3 weeks at #1
Rihanna f/ Calvin Harris - "We Found Love" 4 weeks at #2 10 weeks at #1
Fun. f/ Janelle Monáe - "We Are Young" 4 weeks at #2 6 weeks at #1
Eminem f/ Rihanna - "The Monster" 4 weeks at #2 4 weeks at #1
Poker Face almost didn't make it. The week after it went #1, Boom Boom Pow shoot to the top position. If it wasn't for Boom Boom Pow that year it would have collected 10 weeks at #1
P!nk for Raise Your Glass. (#1 for one week)
Pitbull for Give Me Everything. (#1 for one week)
Miley Cyrus for Wrecking Ball. (#1 for three weeks)
Mariah Carey for My All. (#1 for one week)
Katy Perry for Last Friday Night (T.G.I.F.) (#1 for two weeks)
Avril Lavigne for Girlfriend (#1 for one week)