Using the addAll(listToAdd) method we can append an entire list to another list, like so:

List<String> earlyOptyStages = new List<String>();
earlyOptyStages.add('Prospecting');
earlyOptyStages.add('Qualification');
earlyOptyStages.add('Needs Analysis');

List<String> closedOptyStages = new List<String>();
closedOptyStages.add('Closed Won');
closedOptyStages.add('Closed List');

List<String> allStages = new List<String>();
allStages.addAll(earlyOptyStages);
allStages.addAll(closedOptyStages);

or alternatively, add it like this:

List<String> allStages = new List<String>(earlyOptyStages);
allStages.addAll(closedOptyStages);

With Apex, as you've probably figured out by now, there are a lot of ways to do the same thing. Sometimes there are performance considerations; other times they're just stylistic preferences.