How to make cells with the same width in a table?

This frequently asked question ... Try something like this:

begin{table}[ht]
begin{tabular}{|c|*{2}{>{centeringarraybackslash}p{3em}| }
hline
multirow{2}{*}{a} & multicolumn{2}{c|}{bcbcbcbc}  cline{2-3} 
                   & d          & e                 hline
end{tabular}
end{table}

in preamble you should have

usepackage{array, multirow}

Here's a solution that guarantees that the width of the combined header cell -- which currently contains bcbcbcbc, but which presumably is usually more informative -- is minimal, i.e., that the whitespace padding on either edge of the combined cell is equal to tabcolsep. Observe that the solution employs the w column type rather than the c column type for columns 2 and 3; the w column type lets you state a required width.

documentclass{article}
usepackage{multirow,calc}

usepackage{array} % for 'w' column type
newlengthlenA newlengthlenB
% Retrieve the usable width of the combined header cell:
settowidthlenA{bcbcbcbc} 
% Compute the usable width of the underlying columns:
setlengthlenB{(lenA-2tabcolsep-arrayrulewidth)/2} 

begin{document}

begin{table}
begin{tabular}{ | c *{2}{w{c}{lenB}|} }
  hline
  multirow{2}{*}{a} & multicolumn{2}{c|}{bcbcbcbc}  
  cline{2-3} 
                     & d & e  
  hline
end{tabular}
end{table}
end{document}