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OnTheFence says

Is there a strong reason for reinvesting your gains with the asset that brought those gains?

Absolutely, if you are investing in a passively managed, broad index fund like one modeled after the S&P 500 or Wilshire 5000 indices. If your index already gives you the diversity you seek, it makes sense to reinvest the dividends. I do that all the time with Vanguard's S&P 500 Index fund.

I used to always say "no" and manage it myself. The novelty / hobby factor of managing my investments has worn off, and I find I give it less time. It depends on the investment, but I find that I'm a lot more likely to say "yes" now. As Dan points out, it helps to automatically keep your investments balanced.

Also, the dividend reinvestment doesn't cost anything to execute. If you later want to buy shares of the same stock and do so with a normal brokerage transaction, you pay a fee.

I don't think it's a mistake either way, though.

If it's a dividend growth stock on David Fish's list, I would re-invest. It's a no-brainer. If a quarterly dividend is kicking out $2000 or more, I can see where one would take the cash and redeploy to one of your holdings that is under-valued. Our build up some cash if you see a correction on the horizon...

Isn't the idea of what to you with your dividends a nice dilemma?