hook_nodeapi() is great on nodes, but what can I use on non-node pages?
You have three options:


hook_init() This hook is not run on cached pages - though CSS or JS added this way will be present on a cached page.
hook_boot() Only use this hook if your code must run even for cached page views.
hook_exit() This hook is run at the end of each page request. It is often used for page logging and printing out debugging information. Only use this hook if your code must run even for cached page views.


Performancewise, you will want to avoid hook_boot() and hook_exit(), since they will run regardless of caching. Having one module that implements those hooks brings the familiar warning on the performance page, "The following enabled modules are incompatible with aggressive mode caching and will not function properly: …"

If all you need to do, is add some Javascript, static HTML, or CSS, hook_init() is the best option: the JavaScript and CSS you add will be added to the cache and be present. 

If, however, you need to run actual PHP that is not needed for the rest of the request, e.g. to write a record in a database, or log a line to some file, then hook_exit() is the best option: it will only be called after the page is already served.

If you need to run some setup: e.g. establish a connection with a service, perform access-check and such, then hook_exit() is the best option.