Specifically, I'm referring to being able to have the top 5 search results display as options in a drop down menu while the user types in a search query, somewhat similar to how node reference autocomplete works. It would be great to have such functionality work with Apachesolr.
Depending on your needs, there are a couple of solutions. Probably the closest thing to Apple's Live Search feature is the Finder module. It does not integrate with Apache Solr at this time, however.
I would also keep your eye on the Inline Ajax Search module as Solr integration is on the roadmap. It might need some contributions to push integration through.
A third solution to try is the Apache Solr AJAX module. It might not fit exactly what you are trying to do, however it allows for inline refreshing of the page when queries are entered and filters are enabled.
Acquia offers a solution built on Solr. http://network.acquia.com/services/acquia-search
I would suggest installing the module http://drupal.org/project/apachesolr_autocomplete, this out of the box will let you see Solr's keyword suggestions.
The next issue is showing nodes in the search results and not search terms, there is a hook called
apachesolr_modify_query($query,'apachesolr_autocomplete'); which will allow you to write a custom module to intercept the query as it goes to Solr and tell it to search for nodes and not search suggestions.
The remaining problem you have is simply down to theming the search results so that they look like the regular search.
There already are two theming functions avaliable:
Hope this helps.
At the end of the day you could write the entire module yourself without starting with the base module apachesolr_autocomplete, but I feel it takes a lot of the heavy lifting off you and would be an advantage.