In addition to Werner's excellent answer I'd like to make some remarks.
The indent after a section title (section is used here in a very broad sense, that is, anything with a title) is a question both of personal taste and of typographic tradition.
Tschichold, for example, states that the first indent should be suppressed only after a centered title and that all other paragraphs must be indented (see notes). The Imprimerie Nationale, which the French consider as the supreme guide in typographical matters, states that the first indent must always appear. In British (and US) typography the first indent is usually suppressed. Other national typographic styles follow one or the other trend.
Some language modules for
babel change LaTeX's default of suppressing the first indent: Albanian, French, Galician, Serbian, and (Castilian) Spanish. Polyglossia extends the list: Albanian, Asturian, Basque, Breton, Catalan, Croatian, French, Galician, Greek, Interlingua, Italian, Occitan, Serbian, and (Castilian) Spanish.
The most important criterion to follow is being consistent across a document. Nobody (except perhaps in France) will hold against you a typescript where the "national tradition" isn't followed. However, breaking a well established tradition mustn't be taken lightheartedly, but also not too seriously.
The Spanish module for Babel allows for changing the style (the others don't). For Polyglossia here's what I do when I write a document in Italian:
(yes, I like suppressing the first indent, also after noncentered titles).