This applies to all types of modeling—ordinary least squares regression, logistic regression, linear or nonlinear models, and others. An intercept is almost always part of the model and is almost always significantly different from zero. Note that the test of the intercept in the procedure output tests whether this parameter is equal to zero. If the intercept is zero (equivalent to having no intercept in the model), the resulting model implies that the response function must be exactly zero when all the predictors are set to zero or at their reference levels. For an ordinary regression model this means that the mean of the response variable is zero. For a logistic model it means that the logit response function (or log odds) is zero, which implies that the event probability is 0.5. This is a very strong assumption that is sometimes reasonable, but more often is not. So, a highly significant intercept in your model is generally not a problem.

By the same token, if the intercept is not significant you usually would not want to remove it from the model because by doing this you are creating a model that says that the response function must be zero when the predictors are all zero. If the nature of what you are modeling is such that you want to assume this, then you might want to remove the intercept. This can usually be done by adding a NOINT option.

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