As many as you need for global coverage.
It is a big mistake to invest in one market, e.g. just US stocks (recently, US stocks have become so expensive that I might even recommend smaller than ordinary weight for US stocks). Many index funds do precisely that, and are intended not to be your full portfolio, but rather be a part of a well-diversified portfolio.
An example: you could have 30% USA, 30% Europe, 20% Developed Asia/Pacific, 20% Emerging Markets.
If the index fund is a truly global one and invests too in emerging markets, you could have a good portfolio with just one fund. Do keep an eye on the costs, though. Sometimes, global coverage built from individual funds is less expensive than an all-in-one solution.
If the index fund you're planning to invest to seems global, do remember to check whether being "global" means it invests a large enough percentage to emerging markets.
If the index fund is already diversified, an attempt to diversify more is not needed and will just make your portfolio harder to understand. Generally, it doesn't make sense to invest into two index funds investing to the same market: just select the cheapest one.
I also recommend checking how large the index is. Something like Dow Jones Industrial Average or Euro STOXX 50 would be way too small as an index, because they contain only the biggest of the big companies.
Finally, avoid synthetic funds that track their index through derivatives. Derivatives have a counterparty risk that may be invisible most of the time, but will become visible in a true crisis. Select only funds that genuinely own the shares.
