We'll call individual solutions actions or choices that can be taken by a person independent of what anyone else is doing. Collective solutions are achieved through agreement by a group of people to alter a social rule or institution that shapes people's behavior. It seems that there are at least four senses in which a problem can require a collective rather than individual solution:
Aggregative problems are the most common form of problem requiring a collective solution, but they're also one in which the "it requires a collective solution" defense is fairly weak. In an aggregative problem, a real solution the problem requires everyone to modify their behavior together. This is tied to the claim that reliance on individual virtue will be insufficient to bring about a change in everyone's behavior, so some sort of collective mechanism such as a tax is necessary to motivate and coordinate people's action. However, the fact that something is an aggregative problem does not necessarily rebut concern about people's individual behavior, since, after all, the solution is ultimately about getting every individual to practice that behavior. The more the problem admits of degrees of problematicness (contrast the various possible degrees of global warming with the yes-or-no binarism of nuclear annhialation), and the more individuals' contributions are additive rather than having a threshold at a certain level of participation, individual action makes some contribution to a solution regardless of what anyone else does. Pointing out that something is an aggregative problem just reveals that worrying about one's individual behavior is not enough, so one needs to engage in some more political action (from blogging to protesting) to get others on board as well. And individual action can be an important part of that political action, insofar as it builds a model for the desired outcome.
Tragedies of the Commons
A tragedy of the commons is a situation in which individual action ends up doing no good at all, because it's offset by a corresponding change in others' action. A virtuous shepherd who individually keeps his herd small won't prevent any degradation of the common pasture, because someone else will just expand theirs to eat up that grass. Thus there's no point in worrying about one's own behavior, except as a way of establishing moral credibility, until you can get everyone to agree to the new course of action.
A variant of the tragedy of the commons is the "heightening the contradictions" argument. That is, individual action may alleviate the problem to some degree, but that's bad, because it saps the motivation for pushing for a collective change. If, say, I pay my factory workers well, the benefits to them are offset by the reduced drive that gives toward unionization and a more fundamental and across-the-board restructuring of employment relations. Heightening the contradictions is a tricky argument, however, because it's usually far from obvious that the effects are as described, or that it's ethical to sacrifice the people who would benefit from the individual action (e.g. my factory workers) for the greater good.
With a systemic problem, the issue is the opportunties and rights that are or are not available. So for a person to make their choices as if the rules were different is no substitute for the rules actually being different. A systemic problem is not solved so long as it's dependent on the goodwill of some actors. The difference between a systemic problem and an aggregative problem is whether noblesse oblige alone would be an adequate solution. So energy conservation is an aggregative problem -- unlikely as it may be that this would happen, if it were to come about there would be nothing to complain about. On the other hand, the problem of rape would not be solved (though it would certainly be very much mitigated) if all men voluntarily refrained from having sex with unconsenting partners, because it's still a problem that they have the unexercised opportunity to do so.
With problems that are social responsibilities, the point is to get society as a whole to provide some benefit (usually through the government). So individual provision of the same benefit doesn't actually address the problem. This is often the response of people who advocate an expansive welfare state but are stingy about giving to charity. One could go on to claim that in the absence of society taking responsibility, individual responsibility is still important as a way of alleviating the symptoms in the meantime. This could then be rebutted by a "heightening the contradictions" argument.
Of the options surveyed here, Tragedies of the Commons and Heightening the Contradictions (which I would venture are the least common types of collective problem) are the only ones in which individual action is strictly useless. Nevertheless, pursuing any strategy for social change is not costless, and the costs of social change (time, energy, attention, and resources) can be at least partly fungible between strategies. Thus it may be that (in a given situation) taking individual action, or advocating for others to take individual action, may be substantially less cost-effective than directing those efforts toward collective solutions. (Then again, criticizing others for pursuing individual-level rather than collective solutions may not be cost-effective either!)