I consider market risk, credit risk and operational risk to be the three major forms of financial risk exposure. @jeebs addressed the trade settlement component of operational risk. I would also include the third bullet point that @shane gave in his answer as belonging to the category of operational risk.
Another form of non-financial risk would be political risk, if one is trading in securities that are sourced from a single country e.g. commodities, or traded on a foreign exchange which may become unstable due to political turbulence. Contingency plans would be to trade the same commodity, but perhaps the futures or options on that commodity, or trade the same commodity if listed on other exchanges.
Political risk can also be mitigated by investing in similar but not quite as high yielding securities. For example, if one wanted to invest in developing nations sovereign debt in the past, but have the transaction denominated in a major currency, there were Brady Bonds, which were $US denominated. The same is still true if one is willing to relinquish some return, by buying large corporation bonds from say, Mexico, but denominated in Canadian or US dollars, rather than Peso's.
Finally, there is liquidity risk. If a market is not deep enough, with enough daily (or weekly) transactions, one can get stuck in a position. This can happen in any market, any security type, any where.