Jadakiss featuring Ann Nesby - Keep Ya Head Up
2Pac featuring Outlawz - Baby Don't Cry
2Pac Keep Ya Head Up
Rap songs about not giving up........not sure how much you're going to find in that category. A lot of these songs are usually meant to point out the some of ugly truths about this world and call for a change for the better (or something along those lines). (Personal experiences and or religious themes may or may not be involved)
For example:
Jadakiss - Why
Jadakiss - Why Remix
Sheek Louch - Walk Witt Me
DMX - Slippin
Fort Minor - Right Now
Rhymefest featuring Citizen Cope - Bullet
Young Buck featuring Chester Bennington - Slow Ya Roll
Wu Tang Clan - A Better Tomorrow
Anyways, you can also look up stuff Mos Def, Common, and Talib Kweli.
Truth be told, many (even established rappers) say that Hip-Hop really started to die around 2006; songs with no beats, "Lean Wit It, Rock Wit It" on every other track, more songs with no beats, "This Is Why I'm Hot This Is Why I'm Hot", Soulja Boy, and a shit load of more songs with no beats. Look at Nas' latest album "Hip-Hop Is Dead". Try looking for songs from before '06 and the 1990's.
One more thing, in the future don't bother asking for Rap suggestions on this forum. It's like taking a lit match to a sea of fuel; you're just asking for flames.