If you are thinking about migrating or deploying Sitecore 8 (or 7.5) and use xDB as your new platform for analytics and personalization, Solr will be an essential requirement to make everything work.
Sitecore is designed to work in a multitude of scenarios – spanning from a single-box deployment to multi-server parallelized scale-out deployments.
When you are considering xDB on an on-premises scaled-out deployment (this really starts anywhere where there is basic separation between content management and content delivery) you should consider, that it will not work to its fullest, if you do not include also Solr.
Solr in this case does not need to index and power search for your website content, but rather for the analytics data collected using xDB. In fact, there is an index called sitecore_analytics_index that is being built during the aggregation (a.k.a. processing/map-reduce) service.
While in a single-box deployment, the index is generated by Lucene in Sitecore and is sitting on the same file system that also other components of the use – typically content delivery, reporting, Email Experience Manager (EXM), Engagement Automation and Experience Profile – in a scaled-out environment, the index might be out of reach for some of these components.
In a scale-out deployment, Solr ensures not only indexing of the xDB data, but also proper access for the analytics index to all parties from the Sitecore deployment.
You can configure the indexer separately just for the Sitecore analytics index, without the need to change anything else in terms of search – Sitecore ships with an example config file that you can modify and use to plug Solr in.
UPDATE 18.1.2016: I found a replacement URL, where the role of Solr is described.