If you are looking for tools which will allow you to have centralized logging and capabilities to search and analyze logs, one of the most popular open source tools is combination of Logstash, ElasticSearch and Kibana.

Basically, with this setup you will have one centralized logging server (Logstash) where all your clients will send their logs (via Logstash Forwarder). After that, you will be able to search logs using ElasticSearch and have visual representation of logs via Kibana.

Nice tutorial how to install this stack can be found here.