Rule: The subjunctive (i.e. base) form of the verb is used in that clauses when the main verb expresses a recommendation, resolution, demand, or order.
Examples of errors:
(1) I would probably suggest that they formed a special class for these children.
(2) I think it is better that the child will not be born at all.
This is the only relic of subjective usage in English, apart from were as an alternative to was in unreal conditions (cf. Rule 2.5.2) and in fixed expressions such as So be it, Come what may, etc. The subjunctive is only recognizable as such in the third person singular, except in the case of be, since the other indicative forms are the same as the subjunctive:
I know that you smoke/he smokes (indicative)
I demand that you smoke/he smoke (subjunctive)
The subjunctive is more common in American than British English, and generally limited to formal style, since there is usually an alternative construction with a nonfinite complement available to express the same meaning:
I would suggest forming a special class.
It's better for the child not to be born at all.