Now for no particular reason ...
My top six most memorable "Ending Credits" songs of all time: (off the top of my head anyways)
Super Mario Bros 2 (NES)
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https://www.youtube.com/watch?v=9GB8SSIK0sQ
(The actual credits song starts about 30 second in)
Sure, listen to the Mario All Stars version if you want, but I've always been partial to the NES version myself; it sounds to me much more like something I'd hear playing on a music box. Maybe I'm a bit biased because this was the first game I've ever actually completed on my own, but this is one of the few ending themes I know of that bring a tear to my eye.
Super Mario Land 2 (GB)
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https://www.youtube.com/watch?v=5n3HakhhuEg
OH. MAN. YOU. GUYS. I used to play the final level of this game over and over again JUST so I could listen to this awesome credits theme. This is legitimately the first video game song I ever heard that really made me want to get up and dance to it. And I did. And I'm not ashamed of it.
Super Mario RPG (SNES)
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http://www.youtube.com/watch?v=X-T0DaK5Exw
Awww flip. I just realized that half of the games on my list are all Mario games. Sorry about that, it's just kind of how it happened. Anyways this song is kind of emphasized by the visual sequence that accompanies it, I'm honestly not so sure if this song would be as high on my list if it weren't for that. I'm particularly partial to the part where the stars show you little windows into the all the lives you've touched along your journey. I guess that part isn't /technically/ actually part of the credits; but, eh screw you.
Katamary Damacy - "Katamari of Love" (PS2)
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http://www.youtube.com/watch?v=QU2xHoagCOs
I honestly don't know what to say about this song. I's just loves it is alls.
Kirby Super Star (SNES/DS)
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https://www.youtube.com/watch?v=XF_0aSnvshI
Okay okay okay ... I know you guys are going to just think I'm biased because it's Kirby and I'm ... well ... me. But come ON, how can you tell me that this is not the EPITOME of credits themes. For the DS version, there is actually an unused version of this song that can be found on the OST that is even more amazing:
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http://www.youtube.com/watch?v=4FxHXbmSTjY
And you know what else? One of my favorite all time video game remixes also happens to be of this song:
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https://www.youtube.com/watch?v=89rFeLD3fdc
It's honestly kind of hard to believe that this isn't my number one ending credits theme, but I'm willing to admit that my number one spot may in fact be completely due to bias:
Skies of Arcadia (SDC/GCN)
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http://www.youtube.com/watch?v=JWQh2yHhSCc
I'll be honest, I think the beauty of this song might be lost on people who have not actually played through the game first. Like SMRPG, this song plays while the game shows us glimpses of all the lives that you touched on your journey. And as a follow-up to the ending scene and everything it's just ... I don't really know how to describe how this song really makes me feel, but I swear it makes me tear up EVERY DAMN TIME I reach the end of the game. It's not just that the song itself is wonderful, but how it is so perfectly fitting for the end of this wonderful game. God I wish I were more of a wordsmith so I could more accurately portray to you all how this makes me feel. *le sigh*
[Note:] Just to be clear, I'm not saying these are the ending songs I believe to be the very best out there, just that these are the ones that have personally resonated with me enough to stick with me through the years. If I haven't said something that you believe is better, then either I haven't played the game or the song didn't really stick with me, which is kind of the definition of "memorable".