The first thing you're going to hear is if it ain't broke, don't fix it. Does D-76 do what you like? Do you have any trouble preparing it? What problem are you trying to fix? You'll do better to stick to one developer and learn all about it...
So I've read this opinion quite a bit from many different sources at I guess my question to this is:
Why should a person need a specific technical problem in order to go off and explore other options?
Is there any specific reasoning behind this approach?
When I read the OP, it seemed to me like he/she was just looking to try out something else and wanted some suggestions as to what might be a good alternative to try out. I could be wrong, but it didn't seem like there was a specific problem that was driving the need for a change so much as it was a desire for experimentation. Mind you, I could be completely wrong about this.
Regardless, I don't see the absence of a specific technical deficiency as a reason to not go out and explore other things—even as a beginner. Whether it's trying out different film stocks, different developers, different dilutions, or development techniques, without experimenting, how would I ever be able to make an informed decision about what combination produces the best results to suit my tastes? It would be a bit like using a BIC ballpoint pen without ever trying out a fountain pen, plastic nib pen, gel roller, etc. just because the BIC ballpoint happens to do a competent job of putting your words to paper. Sure, you'd still write your stories, but by never trying out something else, you may be missing some of the joy in the process that you could be having, whether it's an issue of more aesthetically pleasing results or simply a more enjoyable feel. (I use the pen analogy just because I happen to be really picky about my pens so it's the first that comes to my mind. I understand that not everyone will "get it".)
Of course, we always have to set reasonable limits to our exploration if we are ever to get anything done and in the case of photography, I certainly wouldn't recommend that a person switch things up with every roll of film they develop because at that point, you will just completely lack any reference point from which to make a meaningful comparison. But once you get the general gist of what you can expect from a particular developer (or film, or paper, or any number of things), I would definitely say that it's probably good to occasionally try something else out if only for the experience. You may absolutely hate the new things, but at least you'll know that from firsthand experience. And if you happen to enjoy it, maybe you'll decide that you want to make a switch from an informed position.
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As for the OP, I guess you should start by trying to look for the type of aesthetic you enjoy. Once you find a few images in the genre that you shoot that you enjoy the look of, you can try to find out what chemicals and processes were used to create those and use that as a starting point for some experimentation. Just throwing out a question like, "What ___________ would you recommend?" without any idea of what kind of look you're actually trying to achieve makes it a bit difficult for anyone else to suggest something. For instance, a developer like Rodinal is going to give you a really different look from something like Caffenol (Yes, that's a thing. And yes, it involves coffee.)...
D-76 was the first developer I ever used when I had to develop film at a photo lab I worked at years back and like many people have already said, it's pretty much a great standard go-to developer because it will work with just about everything out there. In terms of alternatives, I'm not sure how deep down the rabbit hole you actually want to go because developers range from liquids to powder packets to raw chemical ingredients that you buy separately and measure+mix according to recipes to create developers from scratch. There are so many variations that it's impossible to give a simple answer, but for the sake of providing a potential starting point using only the developers that I actually have some firsthand experience with—which admittedly hasn't been many—and know for a fact would give pretty different results to D-76, I would say check out Rodinal if you're into more pronounced grain and if grain is not really your thing, check out XTOL.
Another major difference between the two is that Rodinal is very forgiving in terms of storage and will pretty much last you forever whereas XTOL is a lot more sensitive to being properly stored and is liable to die on you without warning if you're not careful (and even if you are careful, it has a MUCH shorter shelf life than Rodinal). And when I say without warning, I really do mean without warning. There's no change in color, no gradual loss of effectiveness, no obvious clues... just lots of anger if and when it does happen. Well... I suppose in my case, it was mostly anger from the client and fear of God from me when it did happen to me that one time. Also, to be clear, Rodinal is capable of failing, too, but you pretty much have to be extremely irresponsible and almost purposely work to get it to fail. I've only used Rodinal a few times so far—primarily for stand development—but I've been pretty happy with the look when I've used it. I just personally see it more as a specialty thing so I'm not entirely sure how much you'll enjoy it.
If you give some more detail as to the aesthetic that you're aiming for as well as the amount of work you're willing to tolerate (not everyone wants to mix their own recipes), some of the more experienced members can probably give you some better guidance.
* Edit
I really do need to stop trying to write coherent things at 2AM... it always seems to devolve into mindless rambling. >.<