How to store site wide settings in a database?

Since your question is tagged with database/sql I presume you'd have no problem accessing an sql table for both lookup and management of settings... Guessing here, but I'd start with a table like:

settingName  value   can_be_null   minvalue maxvalue  descriptionTheAnswer      42       no            1       100     this setting does......

If you think about managing a large number of settings, there's more information you need about each one of them than just their current value.

I've used a key/value pair lookup table much in the way you describe with good results.

As an added bonus the table had a "configuration name" column which provided a simple way to choose/activate a specific set of configuration settings. That meant that prod, dev, and test could all live in the same table, though it was up to the application to choose which set to use. In our case a JVM argument made sense. It might make sense to store different "sets" of config settings in the same DB table; then again, it might not.

If you are thinking about file-based configuration, I like INI or YAML. You could still store it in a database, though you probably won't find an INI or YAML column type (as you might for XML).

I would go with the first option -- key/value pair lookup table. It's the most flexible and scalable solution, in my opinion. If you are worried about the cost of running many queries here and there to retrieve various config values, you could always implement some sort of cache, such as loading the whole table at once into memory. In addition to key and value, you could add columns such as "Description", and "Default Value", etc., and build a generic configuration editor that displays the Descriptions, etc., on-screen to help the user edit the config values.

I've seen some commercial applications with a single-row config table, and while I don't have direct experience doing development work against it, it struck me as much less scalable and harder to read.