The Crucible is chock full of so many interesting and complicated characters and a number of compelling themes that your options for addressing it via a thesis statement abound.

You could examine the issue of who is most responsible for the events that take place in Salem, as represented by the play. For example, one might argue that John Proctor is to blame for the tragic events because he had an illicit and illegal affair with Abigail Williams and because he kept the information she shared with him from the court.

One could also argue that Abigail Williams is responsible for the deaths of innocents because of her hypocrisy and apparent lack of conscience—she was attempting to practice witchcraft in the forest and kill Goody Proctor, but then she began to accuse others, knowing it would result in severe punishments.

You could even argue that Deputy Governor Danforth is responsible for the events because he accepts spectral evidence (which cannot be empirically proven) and because he is more concerned about preserving his authority than he is about preserving the lives of innocent people. One could make a similar argument about Reverend Parris.

In addition, depending on what you've studied, you could make an argument about why Miller changed certain facts about the trials, fictionalizing them to some degree. He made Abigail older than she really was, and he leaves no room for doubt that she is conscious and aware of what she is doing and the havoc she is wreaking, all for her own power.

For example, you could argue that Miller made these changes so that the parallels between Abigail and Senator Joseph McCarthy would be more apparent, more effectively commenting on the figurative witch hunt for Communists and Communist-sympathizers in the 1950s and 60s.

You might even focus, simply, on the character of John Proctor, making some argument about his moral ambiguity and its role in the play. For example, you might argue that John Proctor's moral ambiguity—the fact that he does both morally good and morally bad things—leads to the play's theme: that redemption is always possible and integrity is renewable.

Here is one idea:

• A community's crisis is reflected and focused in a crisis of the individual. 

This topic can include a number characters in the play. Hale, Elizabeth, and John Proctor may be the characters of principle concern, as they each experience a crisis of conscience and a test of their integrity that runs parallel with that of Salem as a town/community. 

To build on some of the ideas in #2, I think that a good place to start is picking on any one of the many themes contained in this play. Then you can use that theme to build a thesis that you can defend. Certainly #4 I think makes a valid point by focussing on in some ways what is the simplest theme - that of the truth. But at the same time, it is one of the most complex. You can talk about the differences between the characters that do tell the truth throughout (and die for it) and those that do not, discussing the issue of personal integrity that is so central to this play.

The posts above offer some great ideas with which I concur.  The Crucible really does lend itself to all kinds of writing opportunities.  If I were writing I might consider a simple theme, such as the consequences of not telling the truth in all things.  It's fairly generic, I know, but it's one of those truths which is true in this story and can be true in real life.  Consider the lies told by the girls, Proctor, Elizabeth, Parris, Tituba, and others, no doubt.  The consequences of those lies are death and destruction for an untold number of people. 

Any thesis statement on any piece of literature should be "proveable." In other words, the thesis should be stated in such a way that the paper can provide textual evidence and support of the thesis.

Enotes has an excellent study guide on The Crucible that includes several suggested essay topics, where you can find well-crafted thesis statements: http://www.enotes.com/crucible/suggested-essay-topics.

This answer depends on the topic you truly want to write about. Are you writing a literary analysis paper, a persuasive paper, or an informative essay?

I find some of the most common topics in The Crucible tend to be greed, jealousy, lies, hysteria, hate, good and evil, legalism, and corruption.

A good thesis will include the title of the piece, the author, the topic, and briefly what you intend to demonstrate about the topic. Consider these models:

1. Arthur Miller's timeless classic The Crucible demonstrates the fight between good and evil through an engaging plot, well-crafted characters, and a well-established theme.
2. The Crucible intrigues audiences time and again because it infuses traits of the human condition that every generation contains.
3. The Crucible remains important in society today because the hysteria portrayed in the Salem Witch Trials has potential to corrupt America again.

What can be a good thesis statement that has to do with Salem's paradox in The Crucible?

I think one of the greatest paradoxes is the tension between religion and tolerance. On the one hand, you have a religion that should be based on love and tolerance, since Christianity has at its center the message of the love of God. On the other hand,  you have a religious community that does not show this love and tolerance. In fact, they show just the opposite too often.

Another angle is to connect the story as a contemporary commentary of Miller's day where the "freest and most democratic" country is engaged in the suppression of freedom and democracy. Keep in mind that Miller is writing during the McCarthy era.

What can be a good thesis statement that has to do with Salem's paradox in The Crucible?

There can be several thesis statements that would be able to articulate the paradox of Salem.  One might be that the town's theocratic form of government pursued its own brand of justice in a way that was as far from divine.  Pursuing individual vendettas with the personalized sense of gain is about as far from the sacred that one can get.  Another paradox present could be in the notion of being able to profess a search for truth and justice without any sense of evidence or fairness for those who were accused.  Hearsay and innuendo and gossip replaced fair representation and evidence.  A last paradox would lie in the idea of "forced confessions," or trying to compel confessions out of the accused individuals.