I have quite a few, but a few that stick in my mind are:
Decode:
Well this is not only the song that got me into paramore, It subsequently saved my life by me finding paramore. There's are quite a few parts to this song that make it so special, but it's Hayley's voice throughout and when she singing "woah oh yeah ah" just before the finale chorus. That moment was my escape for so long.
Hallelujah from the Final Riot!:
Need I say more. I mean seriously Hayley belted out those notes that far into the show?? This is why she's in my top singers of all time category.
Emergency from the Final Riot:
I am just dropping FInal Riot! All over this Haha... Well it's for the intro mainly.. I was playing I think it was Call Of Duty with some buddies and one of them was on a major kill streak and the epicness just built as the match continues and the streak was during the intro which was like really really creepy XDD
Soulmate by Natasha Beddingfield: Uhh this ones a little uber personal.. this is the first song I've ever heard that for the first time I was brought to tears. This is for reasons I will not get into now...
Someone gave me an audio recording of a HCT show date and everytime I listen to that entire thing I just get chills mainly because HCT was my only time seeing paramore live and even though it wasn't the same show, it was still the same set and... I still get chills thinking that it actually happened I still daydream sometimes about it to this day..
If I think of any more I'll go ahead and put it here, but that's all I have in my current mind right now...