The primary reasons to invest internationally are high returns and diversification. While foreign stocks are typically more volatile than U.S. stocks, adding international exposure to a portfolio will normally reduce the risk of the portfolio without lowering returns. A portfolio of 80% US stocks and 20% international stocks will likely have similar yields with less risk than a portfolio of 100% US stocks. There is however a historical relationship that investors should be aware of. When the U.S. market goes down sharply, the correlation with foreign markets goes up. In other words, the benefit of diversification is reduced during sharp downturns in the U.S. For example in the crash of 1987, most foreign markets also had large drops. A common wall street adage is "when the U.S. stock market sneezes, the rest of the world catches a cold." But over longer periods of time (months and years) the correlations between markets are low.
The negatives of investing internationally include higher expenses (transactions, management and custody fees), taxes issues, and operational issues (disclosure, accounting, etc.). Additionally, there are added political and currency risks. Investors should also keep in mind that returns from international investing can be heavily influenced by currency movements which can also result in higher volatility. When analyzing past performance, currency effects should be differentiated from local returns. When the dollar is appreciating, returns from foreign investing will be reduced and vice versa.