I have received a really good graduate admission offer from a reputable university in the US but without any funding offer. As I have to accept their admission offer by 15 April and since I haven't yet received offers from some of the universities that I've applied to, so I wanted to know whether it is okay and legal to accept a later offer (e.g., which came after 15 April) with funding, despite having previously accepted an offer (without funding) from a university before 15 April. Thanks.
You ask whether it is "legal", but it is probably not a legal matter. You can drop out of an academic program at any time with no legal consequences beyond paying the relevant fees. Unless your acceptance means signing a contract which specifically requires something on your end, I don't see what you could possibly be legally held to. I am not an attorney but rather a professor, and I can say that in practice no American graduate program would pursue legal recourse against a student in this way barring some truly bizarre, unique set of circumstances.
The relevant questions are rather whether it is ethical, whether it is polite, and whether it is in your own best interests. The first question seems quite clear. Are you really asking whether it is "okay" to rescind your word in a professional context? I would hope that you know the answer.
There may be some situations in which it is so much in your best interests to renege on an offer that it could be worth asking about the possibility of doing so. Most graduate programs in particular are not insistent on keeping students who have decided that they don't want to stay there. But if you're asking about accepting now with the explicit plan of reneging later: I don't really know what to say without it sounding like a lecture on adult responsibility. This is not a specifically academic issue. I can only hope that your life up until now has given you some useful experience.
As several other people have said, as long as your agreement is only verbal, this isn't really a legal question, but an ethical one. When considering whether one can accept an offer like this and then back out with a relatively clear conscience, one mainly needs to consider what you're being counted on to do in the next year, and how disruptive it will be if you don't show up and do that.
It sounds from your description like what you will be expected to do is put your butt in a seat, and sign tuition checks. If that's the case, I think you can pull out without too much guilt if you get a funded offer. Will it really be that disruptive to the program if you're not there? I don't think so. Obviously you should expect to (deservedly) lose any deposit you pay, but I don't think it's likely you'll have any real negative consequences beyond that. Certainly, if I were the graduate director at this "reputed university in USA," I would understand your decision.
EDIT: Incidentally, while I understand it is important that grad schools know who is coming to their program next year in a timely manner, I don't have much patience for moralizing at the OP, since the current situation that they might end up in is a creation of the schools, not the students, and one that the schools positioned to fix, and the applicants are not. We have known for fifty years now how to solve this problem, and haven't done so, even with an extremely successful and smoothly running implementation for medical residents that in many cases the same institutions participate in. I understand that it's an enormous collective action problem, but until it's fixed, people occasionally flaking out on us to take other grad school offers is a very small price we will deservingly pay.
It is possible, legal, and even ethical to do so, though there are some additional stipulations that you will need to follow (see below). Of course, you still run the risk of burning bridges with the people from the school that you end up declining, so think and plan carefully with that in mind.
Most (North American) universities are signatories of the "Resolution Regarding Graduate Scholars, Fellows, Trainees and Assistants" by the Council of Graduate Schools (commonly known as the April 15th resolution), and as far as I know even those that aren't signatories generally follow it's guidelines. You can read the agreement here.
The rules regarding funded offers, including offers after April 15th, are explicitly stated.
Students are under no obligation to respond to offers of financial support prior to April 15; earlier deadlines for acceptance of such offers violate the intent of this Resolution. In those instances in which a student accepts an offer before April 15, and subsequently desires to withdraw that acceptance, the student may submit in writing a resignation of the appointment at any time through April 15. However, an acceptance given or left in force after April 15 commits the student not to accept another offer without first obtaining a written release from the institution to which a commitment has been made. Similarly, an offer by an institution after April 15 is conditional on presentation by the student of the written release from any previously accepted offer.
As far as I know, most schools will (not necessarily happily) give this permission if asked. No one wants to force you to go to their program if you don't want to. But it does make for some awkward at best interactions, and remember that academia is a very small and connection-driven place.
EDIT: I've been awake for far too long and missed the part about it being GRADUATE, not undergraduate. (However, if you're not the original poster and you're applying for undergrad, go ahead and read the rest!)
If you think you might have to reneg on a graduate acceptance, considering the increased effort applied by the college and the possible professional implications later on, it would probably be best to talk to them about it first. At least let them know that it's problematic for you to accept their offer so soon without funding, when others may offer you funding that could make a huge difference. If they cannot at least acknowledge that this is a reasonable concern, they may not be the kind of people whose cooperation you want to chain your future to.
I agree with much of what Pete L. Clark says, but not all.
The ethical implications of accepting an offer and then reneging work like this: In college, you're a number. If your number goes off the list, someone else's number gets onto the list. By accepting a more preferable school and reneging on the less preferable school, you do a service both to yourself AND to the student who discovers that they've been given your place.
The admissions staff is not going to take it personally and get offended. They will get LOTS of letters from students who accepted, but have to call it off. Maybe they decided to join the military. Maybe they had a family issue and they have to take a second job. Maybe they are expecting a child. Maybe they have an illness. Maybe some other thing out of countless possibilities happened. Some students won't even write to inform them of this; they'll just not register for classes. Believe me - colleges are set up for this because it happens ALL the time!!!
Even if someone over there does get miffed, so what? One minute and thirty seconds of them clucking over by the coffee machine is worth N-O-T-H-I-N-G compared to the benefit that would accrue both to yourself, and the student who will take your place. At your age, your sensitivity to social pressure is higher than it will be when you're older. Take my advice - learn to disappoint people when you have to. If you don't, you'll be lead around all your life. Trust me, if you go to a college you don't want to, you're going to look back in ten years and ask, "Why the hell did I give up on the better college - just to save some theoretical person from theoretically disapproving of me? I don't owe it to anyone, to get a lesser education than I can get, just so they don't have to be irritated for a minute. Saving them from that meaningless irritation has cost me so much!!!"
You don't HAVE to make that mistake, so DON'T.
Many departments (at least in mathematics, but I believe also in other fields) have agreed not to "poach" each other's students after the April 15 deadline. If such a department, say at university X, wanted to make you an offer (funded or not) after April 15 and if you've already accepted an offer from university Y, then the admissions chair at X should first ask the admissions chair at Y for permission to make that offer. I would expect that Y would grant permission if Y's offer was unfunded and X's planned offer was funded, but there's no guarantee about that. (When I was graduate admissions chair, in the late 90's, I was once in the position of X, and Y gave permission but was not too happy about it. In that instance, both offers were funded.)