The answer is almost always "YES", you can sue. Anyone can file a lawsuit against anyone for almost anything, fanciful or true or somewhere in between. However, unless your claim is legitimate, your lawsuit will quickly be dismissed.
The better question is: SHOULD I SUE? If that's your question, ask yourself these four questions: (1) Do I have a cause of action? (2) Are there alternatives to litigation? (3) Can I win? and (4) Is it worthwhile to win?
These are discussed below.
"Do I have a cause of action?"
Determine the nature of the complaint and what kind of remedy you seek. You must have an complaint for which relief can be granted. In criminal matters, there's little you can do except refer the case to the relevant authorities (e.g. police) who will then refer the case to a prosecutor. Citizens don't have the authority to pursue criminal prosecutions themselves; they are instead limited to a reporting or evidentiary role. With civil disputes, ask yourself "what kind of injury have I suffered?" (Note: not all injuries are actionable). Do you seek monetary damages? Do you seek to stop a person from continuing a certain kind of wrongful behavior? Was it a one-off injury or is the injury continuing? These sorts of things will determine what kind of action you can bring and whether or not it is within the statute of limitations. N.B.: You can always file suit, but without a valid cause of action, the case will be dismissed.
"Is there an alternative to litigation?"
Litigation should be considered a last-resort option, because you can lose (time, money) even when you win. As such, exhaust the realm of available possibilities before you think about litigation.
Often, a discussion with the other party will suffice. A writing (i.e. a certified letter) has an added benefit: you will have a record of the discussion in case it doesn't solve the issue, which may provide evidentiary dividends at trial.
There are also alternative forms of dispute resolution. Some may be required, e.g. in contractual disputes (binding arbitration is common) or employment discrimination suits (which require EEOC complaints). Many are voluntary -- negotiation, mediation, and non-binding arbitration all are effective at solving disputes -- and some are cause of action-specific. For example, many states offer fee-dispute mediation between lawyers and their clients. This avoids ethics complaints and litigation. Misunderstandings shouldn't cost money or end careers.
"Can I win?"
Having a cause of action is a threshold inquiry -- it's required to get your day in court. However, just having a cause of action doesn't guarantee victory.
First, you have to be able to bring the case financially -- having the resources to win is no small hurdle, and trials can be very expensive. Second, some kinds of cases are notoriously difficult to win. Often, who wins a civil case comes down to (1) who has the burden of proof on an issue and (2) whether they can meet their burden. Usually, the complainant must prove their case by a preponderance of the evidence, but some issues have higher burdens and they can shift if the other side meets their burden too. Lastly, many things about trials are unpredictable. The assigned judge or composition of the jury may matter in close cases. The opposing party may have favorable media contacts or much greater financial resources. Your witnesses may be discredited at trial. These and a myriad other number of things may affect the outcome.
"Is it worthwhile to win?"
Even assuming you have a cause of action, have exhausted all available alternatives, and proved your case at trial, you haven't yet "won". Some states have imposed statutory caps on damages which makes it impossible to recover the amount of your actual injuries, particularly if those injuries are significant and long-term. Obviously, something is better than nothing, but it's a consideration particularly if your lawyer took the case on contingency. Second, you may not be able to collect. If the defendant is be "judgment-proof", i.e. bankrupt or insolvent, or have insufficient assets to pay with, your judgment against them doesn't mean much. Lastly, you still have to pay for the attorney and all of his/her costs. Though some cases allow for recovery of attorney's fees, others don't. Costs can run in the tens or hundreds of thousands of dollars, especially if the judgment is likely to be appealed. All of these things (and more) can operate to make a lawsuit a losing proposition.
To recap, you have to have a valid complaint to file a lawsuit -- one that you can prosecute, prove, prevail, and collect upon. More than that, you need money, guts, and patience to win one. Even if you have these things, if you can avoid litigation through an alternative method, it is generally faster, cheaper, and less stressful to do so.
Asking "Can I sue" has a whole host of sub-questions that an attorney would want to ask you. Generally, these fall into "Sue for what?" "Can you win?" and "Is it worthwhile to win?" If you have nothing to sue for, can't win the lawsuit, or would collect less than it costs to bring the lawsuit in the first place, you don't belong in court.
The suggestions and concerns above are NOT comprehensive. There are hundreds of other considerations to factor in, but are beyond the scope of even a cursory mention in an article like this. Contact a local attorney for advice if you are thinking about bringing a lawsuit.