Is it Oracle or MySQL or something they have built themselves?
Google services have a polyglot persistence architecture. BigTable is leveraged by most of its services like YouTube, Google Search, Google Analytics etc. The search service initially used MapReduce for its indexing infrastructure but later transitioned to BigTable during the Caffeine release.
Google Cloud datastore has over 100 applications in production at Google both facing internal and external users. Applications like Gmail, Picasa, Google Calendar, Android Market & AppEngine use Cloud Datastore & Megastore.
Google Trends use MillWheel for stream processing. Google Ads initially used MySQL later migrated to F1 DB - a custom written distributed relational database. Youtube uses MySQL with Vitess. Google stores exabytes of data across the commodity servers with the help of the Google File System.
Source: Google Databases: How Do Google Services Store Petabyte-Exabyte Scale Data?
YouTube Database – How Does It Store So Many Videos Without Running Out Of Storage Space?