Legacy Answer; Updates from the future below
If already have some Linux/Unix machines in your environment and are comfortable with that format, I'd recommend using Syslog. There are a number of products that will forward your logs to a syslog server for you.
If you're just looking for log collection for legal/compliance reasons, anything will do, really.
Splunk is fairly popular log tool (I think it's based on syslog) that can do a lot of reporting for you. If you want analytics built in, it's a good place to start evaluating. It has a limited free version, but can pay to break out of those limitations.
You can also use Nagios to assist you with your Log Management, especially with some of the plugins and sidecar applications, but I'll warn that it's not trivial to set up.
If you're not afraid of scripting, there are a lot of examples of Logging Scripts at the Microsoft Script Center Repository. (Fulfilling the down-n-dirty requirement...)
If you're not using Splunk, you should use ELK (ElasticSearch, Logstash, & Kibana) as your logging mechanism. While F/OSS like Syslog, it gives you so much more feature-wise. As far as shipping logs, you should use NXLog. It handles Windows Event Logs, and ships them as objects (viewable as JSON, which is how they're stored in ElasticSearch). While each log is slightly larger over the wire, you don't need to write long, painful, and brittle RegEx statements to parse the fields (like you do in order to make use of Syslog, or syslog-formatted logs sent to ELK).