The stock-market rally presents a difficult choice for some individual investors: Miss out or risk getting in at the top.

The scars of the financial crisis have left many wary, even as the second-longest bull run in S&P 500 history has added more than $14 trillion in value to the index since it bottomed in March 2009, according to S&P Dow Jones Indices. Yet there are signs that caution is dissipating.

Investors...