Syslog and event management can grow into a large topic and ultimately lead into analytics and SIEM.
The original syslog daemon is syslog on linux, but most distributions come with rsyslog theses days and is very flexible in sorting and filtering messages. But it is all through the CLI.
If you want a UI to investigate logs then again there are lots of open source tools, to get started download security onion http://blog.securityonion.net/p/securityonion.html , install into a VM and have a look at ELSA.
You can also checkout LogStash as well, but it is a more involved install.
Then there are all the commercial offerings that you can look and a few give a freemium model.
Cheers
Dan