There are many databases for many things.
https://datomatic.no-intro.org/ is probably the best.
"a direct back-up of the an actual game" can also be a bit nebulous, especially as time goes on and standards for it vary.
No-intro above aim for the purest versions of a given game. The closest to a cartridge/optical disc/whatever that you can get. For some though they go too far -- towards the end of the DS lifetime it was noted that a part of the header was not filled with 00/FF any more and instead some data that the DSi (later also 3ds) used to determine it was a good (pure DS) game was included, all the earlier stuff being put on a whitelist. Older dumpers ignored this and continued to assume 00/FF filled. It was not necessary to run the game, no flash cart cares* and no emulator or hardware clone will ever likely care unless they really miss the point and leave/force security in there.
*technically the makers of such devices might have cared for their future products (
https://hackmii.com/2010/02/lawsuit-coming-in-3-2-1/ ). Instead they were owned from the ground up so nobody minds.
Hashing algorithms by their very definition as (good) hashing algorithms will change output drastically if a single solitary byte changes (see avalanche effect if you care about the maths behind it all). You can twist this and do checks on individual files within a ROM (some of the MAME dats do something almost like this) but I have never really seen anything like it for the rest of the gaming world. Let me also tell you about the rest of the gaming world and the history of warez scenes. Short version. They, like many, only want something that works. If they can rip, compress, relink, alter or not have to deal with certain standards** they often did just that. The relinking part is key as well -- at one point in time I could not buy many discs for almost nothing in a pound/dollar store and instead they cost lots, good ones cost more still and super nice ones (either 80 minute CDs compared to 74, DVDRs compared to CDRs or single layer DVDRs compared to dual layer DVDs) more still so the kind folks would rip extraneous stuff and package it up into something that fit on smaller discs/drives or took less to download and this was considered normal and good behaviour. Indeed up recently it was all but mandatory to crack the anti piracy on the game you were releasing, and many today will still call for such a thing. This also skips over the idea of intros but... there is a reason it is called no-intro above.
Such a thing can come back to bite people in the arse -- all the stuff I just described happened by default in the original xbox scene, come the 360 and its security was a bit longer in being defeated so all those nice modified games needed to be redumped to work on it with the more limited DVD hacks. It appeared after a fashion on the Wii as well with the various takes on WBFS and iso manipulation there (everything from scrubbing on down). For the Wii I did see something interesting the other month
https://gbatemp.net/threads/new-wii-unscrubber-swiit.511181/ , and it also technically makes me a liar as that means I have seen a file level hashing program made and even taken as far as being able to reconstruct isos but don't get used to it. Speaking of the 360 security you might also want to have a look at the evolving security it saw and approaches used there, or if you just want a tool ABGX360 is what you want.
As for "there should be cracks" you might like to see all the fun and games people on the DSi and 3ds are having trying to run games where the anti piracy patches are all tied up in closed source flash carts, would have been a non issue should those calling for all cracks, all the time had their way.
Some dat files will include every version they can find (up to and including hacked and translated versions) and thus give you some idea. I have not seen these too popular since the GBA era though and I don't think it even really made it to the end of that. Goodtools/goodmerge is probably where I would start for that. If you see dats with things like [!] and [t+somelanguage] in their names they might well have something like this.
**the PS1 era was famous for there being a billion competing formats for isos (see the lists things like magiciso, ultraiso and such like handle) and much like we are still using closed chat protocols you can't run your own servers for today people back then did not pick the future proof option and might have picked one to work with their needs (several makers of such programs unofficially positioned themselves to work where more basic methods would have failed). To that end PS1 games will easily come in iso, bin+cue, nrg (Nero's format, though one included with seemingly every CD writer back when), cdrwin and clonecd formats to name just the popular ones, also not wanting to go too far and cause myself/others that suffered the times to start rocking in the corner. So you downloaded... nice iso ripping tools and ripped the games from your personal collection. Great. Now all the old ROM hacks and tools made for such things might struggle if they are aimed at the far more popular/available legacy Scene release probably don't work or will require a tonne of effort (and ideally a copy of the legacy Scene release) to be made to work.
So no. No simple answer here. First you get to pick your camp, and while people say "I want the purest" in many cases they don't care and maybe instead just want something with the functional appearance of stock and not necessarily the OCD pedant's then most reasonable interpretation (because tomorrow someone might find something that will rip those hidden/inaccessible/encrypted sectors that nobody actually cares about --
http://www.its.caltech.edu/~costis/sgb_hack/ ) and may even be happy with the Scene rips that were made at the time (if they made a ripped version*** they tended to also release a more complete version for those with the space/money to burn on discs) and actually work very well.
***yes you can rip a disc/ROM from its original media and yes you can rip files or sections from an iso/ROM to make a smaller version, the resulting product being known as a rip in the parlance of the times. Yes it got confusing and yes it still does confuse.
Oh and do you do boxart and manuals? Because that is also a thing for some, said some including those that might make some of your favourite emulators (
https://arstechnica.com/gaming/2011...-3ghz-quest-to-build-a-perfect-snes-emulator/ ,
https://byuu.org/emulation/preservation/ ).
