The cost plan is a crude approximation of the actual query cost. Sometimes, the query planner makes a terrible guess. Your resident DBA won't appreciate being sometimes paged at 3 AM on a Sunday. A good strategy is to freeze the query plan once you have sufficient sample size of data in the involved tables.
Perhaps not every aspect of the query plan can be dictated, but both MySQL and Postgres (with pg_hint_plan) allow you to specify hints that enforce specify join order and scan behavior for the tables in your query, which is where the majority of "unexpected change in query plan" problems will arise. As for SQLite, I'm less familiar with the knobs available for query tuning, but a cursory Google tells me that join order is respected when using CROSS JOIN, and index usage can be forced with INDEXED BY/NOT INDEXED.
