The purposes of this question is to collect examples from theoretical computer science where the systematic use of computers was helpful
- in building a conjecture that lead to a theorem,
- falsifying a conjecture or proof approach,
- constructing/verifying (parts of) a proof.
If you have a specific example, please describe how it was done. Perhaps this will help others use computers more effectively in their daily research (which still seems to be a fairly uncommon practice in TCS as of today).
(Flagged as community wiki, since there is no single "correct" answer.)