If I have a few UNION Statements as a contrived example:
SELECT * FROM xxx WHERE z = 1
UNION
SELECT * FROM xxx WHERE z = 2
UNION
SELECT * FROM xxx WHERE z =
If you care what order the records are returned, you MUST use an order by.
If you leave it out, it may appear organized (based on the indexes chosen by the query plan), but the results you see today may NOT be the results you expect, and it could even change when the same query is run tomorrow.
Edit: Some good, specific examples: (all examples are MS SQL server)
Dave Pinal's blog describes how two very similar queries can show a different apparent order, because different indexes are used:
SELECT ContactID FROM Person.Contact
SELECT * FROM Person.Contact
Conor Cunningham shows how the apparent order can change when the table gets larger (if the query optimizer decides to use a parallel execution plan).
Hugo Kornelis proves that the apparent order is not always based on primary key. Here is his follow-up post with explanation.