Games With Good Songs?

SONGS WITH LYRICS:

The Witcher 3 — "Wolven Storm"
Alan Wake — "Balance Slays the Demon" and "The Poet and The Muse"
TellTale's The Walking Dead Season 1 and 2 — "Take Us Back", "Remember me", "In The Water", "In the Pines."

SCORE:

Deus Ex and Deus Ex: Human Revolution
Mass Effect
Halo — songs like "The MJOLNIR mix" and "Blue Team"
Crysis 2 and 3 — songs like "It was never just about the suit" and "Crysis 2's Epilogue" are simply amazing.

Hotline Miami

METAL GEAR RISING: REVENGEANCE
Includes some of the most badass boss themes ever

Dragon Age: Inqusition - Sera Was Never & other tavern songs
Vampire the Masquerade: Bloodlines - A Smaller God - Darling Violetta, Swamped - Lacuna Coil, Isolated - Chiasm and probably others I can't remember
and of course Omikron: Nomad Soul with soundtrack by David Bowie

Deus Ex: Invisible War - https://www.youtube.com/watch?v=o1w-e8wpKo4
One more for Alan Wake, Children of the Elder God: https://www.youtube.com/watch?v=7M1k1tgq87g

Brutal fucking Legend.

First that comes to my mind: Final Fantasy X - Otherworld

Transistor OST is <3 https://www.youtube.com/watch?v=-zA1jRmAYfU

Guitar Hero series

Life is Strange
Transistor
Bastion
Oh and Metal Gear Solid V The Phantom Pain

Alan Wake, Tales From The Borderlands, Life Is Strange.

Max Payne 2: Late Goodbye https://www.youtube.com/watch?v=GCj-I4LoqtQ

(how did I not remember this immediately...)

The Wonderful 101 - The Won-Stoppable 100

F E Z

https://www.youtube.com/watch?v=mV7njzhLAsQ

all final fantasy games

Call of Juarez : Gunslinger - O, Death O, Death Soundtrack

Death Goat's got a lot of songs with words in it.
Vampire: The Masquerade – Bloodlines's good too (e.g Tiamat - Cain)
Gray Matter (e.g Menu Song).
Brütal Legend
If it counts, loved SpaceChem's ominous pseudo-latin (I think) chants
Not 100% sure but I think Savant - Ascent had some songs with words in it.

EA's sports games often have good songs
oh, and Guitar Hero / Rock Band is there really a difference?

If you like rock/metal then Devil May Cry 3 (for songs with lyrics "Devils Never Cry" in particular and most of the game's boss and battle themes for just a really awesome soundtrack) and Devil May Cry 4 (lots and lots of awesome songs, some with lyrics) are the first games that come to mind. :)

The Serious Sam series (3 in particular) has a lot of good ones too (though very few are with lyrics).
No Lyrics there but Painkiller, Giana Sisters: Twisted Dreams, Super Meat Boy have really really really good soundtracks. :D

Those are only the first that come to mind. ^_^

Shatter is pretty solid. Every track is stellar if you like any of them, at least.

edit: I didn't read.

I liked The Evil Within's opening song, though. No idea if you mean a song with lyrics somewhere in the game or if it's played throughout the game. Persona 4 is probably my favorite from what you're asking then.

x2 Edit:
Life is Strange has a good variety.
Tiny and Big is one too and you can cycle through which songs you want to play, too.

since i had some free time, here are some songs i had in a playlist :3

alan wake https://youtu.be/7M1k1tgq87g
bastion https://youtu.be/YK8LPtbdsEM
borderlands https://youtu.be/9er3dEHe_PI
borderlands 2 https://youtu.be/dmzbep3BWbY
broforce https://youtu.be/-0qlgvsQ9_o
divinity: original sin https://youtu.be/StLLp4Jgw2o
guild wars 2 https://youtu.be/dlBvKzc8Odo
mass effect 1 https://youtu.be/sUKiOcV1SSc
max payne 2 https://youtu.be/GCj-I4LoqtQ
mirror's edge https://youtu.be/YP3M9_gICsc
rebel galaxy https://youtu.be/A_xo0W3jaCg
tales from borderlands https://youtu.be/hGqW68-Mo2c
transistor https://youtu.be/8keRZa7hAqM
witcher 3 https://youtu.be/823yuWz0lto

- unofficial
elder scrolls online https://youtu.be/a-HyYklN55U
mass effect https://www.youtube.com/watch?v=re32xnyYP3A
witcher 3 https://youtu.be/c0trGRJs_IU

Bastion is beautiful

Read Dead Redemption such a great way of using music, this song was perfect as you rode horseback into Mexico.

Final Fantasy X-2 one of its few redeeming features for me was this song.

that I can think of, all of these have either good music or excellent music in my opinion.

Rome (1) Total War
Fallout (3, New Vegas, 4) overall has good music and songs. I personally dislike a few, but overall it's good and a few quite excellent.
Portal end song is nice
Skyrim has a nice intro song
Medieval 2 Total War
Civilization IV

Rocket League has lyrics in its songs. I don't know if there's lyrics in all of them but I do know some of them do.