Depends on the volume of data you're logging and if you need to do real-time analysis on it. Certainly not for all use cases but where I work we're doing a lot

Depends on the volume of data you're logging and if you need to do real-time analysis on it. Certainly not for all use cases but where I work we're doing a lot with LogStash (on Elastic) to "do business work" on data streams that are coming in at up to 1Gbps. Since we have it in place already for other business needs we throw a lot of app telemetry data at it as well and have rules for processing events and issuing alerts. For more down-to-earth scenarios, log4j (which can be used from Python and other languages) along with several Apache logging projects (eg: log4php) are good options. If you're on .NET I would look first at Serilog.