"Involved" is something of an imprecise word since there were a number of neutral countries, but for the most part they were involved, whether they liked it or not, to some degree or other - whether through non-military support, trade, or, of course, being invaded. I've written about The Swiss and The Irish before, which you will likely find of interest, and our FAQ has more entries on several of the neutral powers, such as Spain and Sweden. There are a few which lack solid entries, Portugal perhaps being the most notable, but also lacking Afghanistan and Tibet, but I would recommend that you consider re-asking to focus on a specific country if you are interested in them.