Scenario: You need to display a component in as much space as it can get.
If it is the only component in its container, use GridLayout or BorderLayout. Otherwise, BorderLayout or GridBagLayout might be a good match.

If you use BorderLayout, you will need to put the space-hungry component in the center. With GridBagLayout, you will need to set the constraints for the component so that fill=GridBagConstraints.BOTH. Another possibility is to use BoxLayout, making the space-hungry component specify very large preferred and maximum sizes.

Scenario: You need to display a few components in a compact row at their natural size.
Consider using a JPanel to group the components and using either the JPanel's default FlowLayout manager or the BoxLayout manager. SpringLayout is also good for this.
Scenario: You need to display a few components of the same size in rows and columns.
GridLayout is perfect for this.
Scenario: You need to display a few components in a row or column, possibly with varying amounts of space between them, custom alignment, or custom component sizes.
BoxLayout is perfect for this.
Scenario: You need to display aligned columns, as in a form-like interface where a column of labels is used to describe text fields in an adjacent column.
SpringLayout is a natural choice for this. The SpringUtilities class used by several Tutorial examples defines a makeCompactGrid method that lets you easily align multiple rows and columns of components.
Scenario: You have a complex layout with many components.
Consider either using a very flexible layout manager such as GridBagLayout or SpringLayout, or grouping the components into one or more JPanels to simplify layout. If you take the latter approach, each JPanel might use a different layout manager.