Owning multiple funds with close correlations is mostly wasted effort and potentially self-deception. Owning multiple funds with a significant correlation spread can be helpful in reducing overall portfolio volatility.
Here is a table with the 6-month correlation of daily returns of selected iShares ETFs with at least 6 months of history (as of April 21, 2009), as rendered by the iShares website.
It reveals how the various funds have behaved during the past two quarters which saw so much portfolio value destruction. Longer periods of time for correlation should generally be considered, but it is interesting to see how funds behaved during these violently turbulent times.
Here is a shorter list of iShares ETFs showing their 3-year correlation: