Ah yes. Yellowcard was one of the bands that got me listening to the type of music I listen to today. (I started listening about 2 years ago after they released The Underdog EP.)
As a side note, Yellowcard is considered Pop Punk more than it is considered Indie Rock. (Categorizing music is ALWAYS fun... *sigh*).
Anyhow, if you're starting to get into Pop Punk music, check out Starting Line, Fall Out Boy, and Rufio if you want some classis bands.
If you want true Indie Rock, go with Death Cab for Cutie, Mars Volta, Honorary Title, As Tall As Lions, and The Decemberists. All amazing bands. As Tall As Lions is like this child I could never be apart from. Check out their full length Lafcadio and be amazed.
If you want some straight up Punk kind of music with some spins of Indie and Pop, check out Brand New, Northstar, June Spirit, Further Seems Forever, and Coheed and Cambria.
And for some more laid back stuff, go with Copeland (oh gosh, Copeland is beautiful), Cool Hand Luke, Lyndsay Diaries, and Damien Rice.