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I've noticed that there are people who can recgonize the notes played in melodies of songs that they didn't right. As in you could listen to the chorus of a song and know what notes are being played. How is this acheived? How can I train my ears/brain to do the same? It would be very helpful to me as a becoming composer.

Well I can't do it for every note, I can recognize every time an A key is played. I began doing this when I found that the lowest I could sing was an A note, then I just was able to gauge myself from their. My guess is that you would have to train yourself to do all of them.

I'm not sure how people can do it. I can do it in a pretty primitive form, that is to say I can but it takes me a while to figure out what notes are being played. I'm glad I can do that much, though, since I do play piano. I'm better at juding intervals than actual notes. But unless I'm wrong, it's something you're born with and can't learn.

You can learn it, it's just much harder to do it as you get older.
What you're talking about when you mean judging notes by intervals is called relative pitch.
Being able to pick out notes right away is known as perfect or Absolute Pitch

I'm pretty sure you can learn it... It really helps if you learn to play an instrument, or so I've heard.

Well, unless you're exposed to notes and actually know what they are, you can't really learn. Playing an instrument obviously provides both of those.

Well, you can train yourself, like find notes on the internet and play them until you recognize them in a second. Luckily, my mind instantly relates a note to a color, so it's pretty easy for me to know what key is played such as the song, Wish You Were Here by Pink Floyd. I first imagined light green (G), red ©, yellow (D), and dark green (A); then I later found out that these were they keys used.

Actually, you also need a lot of practice to be really efficient at it. I've been at it for years, so it's a piece of cake for me.

But not so when I just started, ja?

You can learn relative pitch easily (or so I've heard) by learning certain patterns between notes by memorizing certain well known music.
Refer: http://en.wikipedia.org/wiki/Ear_training

As for absolute pitch.. you wouldn't be able to develop them unless you've had intensive years of music training and instrument playing. I know people who practice for hours every day and still don't have it.

There's perfect pitch and relative pitch.

You're either born with perfect pitch or not. Sorry.

BUT you can TRY to get perfect pitch, but that's actually called relative pitch. It's good enough.

Relative pitch is just, let's say, you can sing a melody no matter what key you're in...

Or somebody gives you a 'Do', and you can spit back a 'La' regardless of what the actual note is.

Kinda like transposing in your head. Except you're not really transposing...

So then... How does one develop relative pitch?

I did five musicals over four years, joined my school's chorus, and took up piano. That seemed to work.
Singing really helped, as did playing the piano... you have to know what the notes are as you're hearing/producing them in order to get anywhere, in my opinion.

It's gotten to the point, for me, where I have a few hours worth of video game music stored in my brain with nary a sheet of paper used.

And... does that give you the ability to recognize notes?

Well, it's all learned by ear, so yes.

Unless you have perfect pitch or you have relative pitch, then it's hard to know video game melodies' notes by heart (you might know the general idea of it, but it's probably off a few steps).

To get relative pitch.. the best way is to play a musical instrument.. or sing in a choir or something; that'll definitely get you relative pitch.

So, let me get this straight. If I said "hum an A flat", or played a scale and said "pick out the D sharp", you could do that? I don't think you could identify notes by name after any amount of time just by listening to music. I don't know how you would figure out which note was the A flat or D sharp unless someone or something told you. Note values don't exist in nature, they are man-made. There's a massive difference between storing hours of music in your brain and being able to identify the notes used in it.

Listening to alot of music can certainly help though, because as soon as you find out the scales from G through A you can identify changes alot easier because you've heard it so many times. Although you are still very right in my opinion that there is a difference between being interested and being educated..

At best by listening to a lot of music you would recognize those notes as "this note" and "that note" but not "A sharp" or "B". You can't just listen to a note 5000 times and be able to identify it by letter without someone or something defining the corresponding letter.