I have just installed lijit on a couple of sites and so far, I'm delighted with the features and performance. Lijit uses the open source Lucene search engine to power its searches. It provides fast accurate results with contextual extracts of the search terms in a lightbox overlay. This is a nice feature as it allows you to search and research items without leaving your current page.
Lijit can override/hijack your wordpress native search, so that you can still use the existing search forms and widgets on your sites. However, lijit goes much further than simply offereing a superior search engine; You can also add any number of sites to your search index, including social networks that list your content. This allows you to create your own 'network' of material that's available in a seperate tab in the results. The search engine has another cool feature which returns a small list of related items to your search. So if the first result failed to provide the goodies, the other links are close to hand to conveniently investigate.
Lijit provides a wealth of statistics that are easy to understand, clearly presented, relevant and useful for analysis. This is an excellent feature that also shows some basic details in your search box, such as recent visitors from searches and the most used search terms.
I've used Lijit for only a few days so far. There are a few minor issues that need resolving, but I'm getting very helpful feedback from their support. Right now it's the best search/ research tool I've used for wordpress, giving fast, contextual data that adds a powerful in road to your website content.