Generally speaking you're making a decision between fast read times (e.g. nested set) or fast write times (adjacency list). Usually you end up with a combination of the options below that best fit your needs. The following provides some in depth reading:

• One more Nested Intervals vs. Adjacency List comparison: the best comparison of Adjacency List, Materialized Path, Nested Set and Nested Interval I've found.
• Models for hierarchical data: slides with good explanations of tradeoffs and example usage
• Representing hierarchies in MySQL: very good overview of Nested Set in particular
• Hierarchical data in RDBMSs: most comprehensive and well organized set of links I've seen, but not much in the way on explanation

Options

Ones I am aware of and general features:

1. Adjacency List:
   • Columns: ID, ParentID
   • Easy to implement.
   • Cheap node moves, inserts, and deletes.
   • Expensive to find level (can store as a computed column), ancestry & descendants (Bridge Table combined with level column can solve), path (Lineage Column can solve).
   • Use Common Table Expressions in those databases that support them to traverse.
2. Nested Set (a.k.a Modified Preorder Tree Traversal)
   • Popularized by Joe Celko in numerous articles and his book Trees and Hierarchies in SQL for Smarties
   • Columns: Left, Right
   • Cheap level, ancestry, descendants
   • Compared to Adjacency List, moves, inserts, deletes more expensive.
   • Requires a specific sort order (e.g. created). So sorting all descendants in a different order requires additional work.
3. Nested Intervals
   • Combination of Nested Sets and Materialized Path where left/right columns are floating point decimals instead of integers and encode the path information. In the later development of this idea nested intervals gave rise to matrix encoding.
4. Bridge Table (a.k.a. Closure Table: some good ideas about how to use triggers for maintaining this approach)
   • Columns: ancestor, descendant
   • Stands apart from table it describes.
   • Can include some nodes in more than one hierarchy.
   • Cheap ancestry and descendants (albeit not in what order)
   • For complete knowledge of a hierarchy needs to be combined with another option.
5. Flat Table
   • A modification of the Adjacency List that adds a Level and Rank (e.g. ordering) column to each record.
   • Expensive move and delete
   • Cheap ancestry and descendants
   • Good Use: threaded discussion - forums / blog comments
6. Lineage Column (a.k.a. Materialized Path, Path Enumeration)
   • Column: lineage (e.g. /parent/child/grandchild/etc...)
   • Limit to how deep the hierarchy can be.
   • Descendants cheap (e.g. LEFT(lineage, #) = '/enumerated/path')
   • Ancestry tricky (database specific queries)
7. Multiple lineage columns
   • Columns: one for each lineage level, refers to all the parents up to the root, levels down from the items level are set to NULL
   • Limit to how deep the hierarchy can be
   • Cheap ancestors, descendants, level
   • Cheap insert, delete, move of the leaves
   • Expensive insert, delete, move of the internal nodes

Database Specific Notes

MySQL

• Use session variables for Adjacency List

Oracle

• Use CONNECT BY to traverse Adjacency Lists

PostgreSQL

• ltree datatype for Materialized Path

SQL Server

• General summary
• 2008 offers HierarchyId data type appears to help with Lineage Column approach and expand the depth that can be represented.