If you are not limiting yourself to the old consoles then yeah the GBA and DS each have a fairly extensive sound format that is shared by the vast majority of games on the respective systems.
The GBA sound format is commonly known as Sappy, some people know it by other names but if you wander into anywhere versed in GBA hacking and say I want to know about sappy then people will at least know what you are talking about.http://www.romhacking.net/documents/462/
Folks working in fire emblem, advance wars, some golden sun stuff (though they took things in a fairly different direction) and pokemon have some worked examples, however some of them have some very odd ideas about things at times (it was about the time I was watching someone explain fixing pointers using a tile editor that I wondered what had led me to that point).http://forums.warsworldnews.com/viewtopic.php?t=2002
is good and http://www.feshrine.net/ultimatetutorial/
has a bit as well.
I did have a bit in my GBA and DS hacking docs (linked for DS in a second) but I find sappy music hacking terribly boring so what is there is pretty minimal. On the other hand it should have links for the various downloads and tools used.
Some of the better hacks are probably the golden sun voice acting experiment and the Final Fantasy audio restorations for the GBA versions of 4, 5 and 6. The author is a regular around here as well so there is that.http://www.romhacking.net/hacks/657/ http://www.romhacking.net/hacks/563/ http://www.romhacking.net/hacks/969/
With a bit of effort you can turn a midi or some other tracker format into something the engine will recognise and have it play in a game.
The DS sound format is called SDAT. Percentage wise it is probably even more popular than sappy is on the GBA.http://www.romhacking.net/forum/index.php?topic=14708.0
is my hacking docs for the GBA and DS, it covers quite a bit of stuff you can do with SDAT.http://www.romhacking.net/documents/469/
if you want some more low level stuff.
What you can do varies with the game or the level of hacking you want to go in for (there is a streaming audio format known as STRM that the compiler leaves out if the game does not use it, the DS does feature hardware decoding for (AD)PCM though so you can hack in something to pipe it to that instead). On the other hand if you are more concerned with tracker/sequenced audio then you can quite easily convert and insert midi into it and basically every game with SDAT will use SSEQ streaming, you may have to change the instrument bank but that is nothing too drastic either.
SDAT is then threefold
STRM streaming audio, not terribly commonly seen but very much part of it all.
SSEQ sequenced audio, flanked by SBNK sound banks
SWAR/SWAV. Technically this is wave but the sizes available are such that it is more samples and SFX type things, very occasional a short monologue (Castlevania portrait or ruin).
They various get packed together, have a header file that determines a lot and a bit more besides but if you are at all used to computer audio it should not pose much of a problem.
Equally when games do not use the above formats on the two systems it is usually a common format in general audio (everything from wave to tracker formats like XM), something very closely related to those (headerless wave files/raw PCM in some cases on the DS) or something common in game dev and likely well known/documented (cri middleware's ADX format is seen sometimes on the DS). I cover some of the alternatives seen on the DS in my docs and there might be more in http://gbatemp.net/threads/the-various-audio-formats-of-the-ds.305167/