Make It Stop (September's Children) by Rise Against always makes me tear up a bit, but at the same time keeps me fighting.
Better Off Dead and Kick Me, both by Sleeping With Sirens, are solid songs. One (Kick Me) is THE BEST angry song I own, and trust me when I say I own a lot of angry songs, and other is almost an angry song about no one seeing your pain, even after you've made it perfectly clear.
View from Heaven, by Yellowcard is also a good song as a goodbye to a loved one, be it friend or family, but it's very well written and I love the violin that the band includes.
Bro Hymn is another good one about losing friends, but it's a bit basic, as it was written by Pennywise. It's still very good.
Knives and Pens, by Black Veil Brides, is very good. It alternates between singing and screaming, and it's really about how you can choose between destruction (knives) or creation (pens.) Plus, Andy Biersack has an amazing voice.
Trophy Wives has a bunch of good songs. They're a small band from Providence, RI that I hung out with at Warped Tour. Genuine group of guys, very good performers and songwriters, I'd compare the quality of the writing to majorly successful bands like Fall Out Boy. Just check out a few of their songs and see what you think of them.
The entire Misadventures album by Pierce the Veil, that shit is good (the bassist of Trophy Wives agrees with me.) Texas is Forever is especially amazing, as is Gold Medal Ribbon. I'd also suggest Match Into Water and Bulls in the Bronx, as well as King for a Day if you enjoyed Kellin Quinn (Sleeping with Sirens)
Stay Together for the Kids, by Blink-182 is the bomb, and I quite like how soft-spoken it is, relatively speaking. You can feel the pain of coming from a broken home in their voices.
All Downhill From Here and My Friends Over You, by New Found Glory are both good, energetic songs. The band is a bit immature and it shows in their song lyrics, but they're still good songs.
Therapy, by All Time Low is very good, it feels like I wrote it, it describes my emotions so well. The entire song was written by Alex about having to go through therapy and coping with his feelings after losing his brother, and it's incredibly heartfelt.
Finally, G. I. N. A. S. F. S, by Fall Out Boy, is INCREDIBLY good and cleverly written, Pete being Pete and all that. Disloyal Order of Water Buffalo is very good as well, as is What a Catch, Donnie, and although a little childish, Lullabye.