Which runs count when a batter is dismissed?

Under Law 18.8, when a batter is out:

• Penalty runs awarded to either side always stand, including the 1-run penalty for a No ball or Wide.
• No other runs are scored, except:
  • Run out: runs completed before the wicket was fairly broken also count. (If the striker has a runner and is run out under Law 25.6.5, runs completed by the runner and the other batter are disallowed.)
  • Obstructing the field: runs completed before the obstruction count, unless the obstruction prevented a catch, in which case only penalties count.

So if the striker is caught, any runs the batters ran before the catch is completed are not scored. Law 16.6.2 applies the same principle to a winning total: runs completed before a catch from which the striker could be out don't count towards it.