Just as an example of how awesome Elasticsearch is, you can trivially segment your storage tiers (say, SSD versus HDD) and then easily move older data to other storage, with a single command.
They have a log-specific handler called Logstash, and a dashboard system called Kibana (which is sorta neat but the UI seems a big laggy in my brief experience). Apparently some folks use Logstash/Elasticsearch to record millions and millions of events per day and ES does a great job.
If you want hosted, check out Stackify. I'm totally blown away with the product (no affiliation other than being a new user). You can send log info to them and they'll sort it all out, similar to Splunk, but not ridiculously priced and no dealing with terrible sales teams. But it gets better - they offer all sorts of ways to define app-specific data and metrics, so you can get KPIs and dashboards just adding a line or two of code here and there. It's a lot easier than running your own system, and it looks like it can make ops a ton easier.
Another hosted service is SumoLogic. I only used them for logging, but it seemed to work well enough.