Any tool to monitor ArcGIS Server Usage
System Monitor Tool from Esri is a great application for monitoring your services in more detail, ive used it a fair bit over last few months and its well worth installing.
It has a browser based console, stores all the metrics in MongoDB, good docco for both installing and using it. Monitors not only your ArcGIS Server and its services, but can look at the CPU/memory/resources of multiple machines, your database, ping HTTP, and you can view the metrics in nice charts and reports, get sent email alerts when resources are running low, along with much more.
Highly recommend it.
I can really only expand on your 1st point (3rd party solutions). At this time the current version of Server (10.2) only has the number of running instances and number of requests available from the REST Admin. To the best of my knowledge there wont be any sort of "statistics" like you're asking for in the 10.2.1 release upcoming, but it is something that has been talked about and is being considered.
At this years UC (2013) I did a session on Python against the REST Admin API for Server. You can download it here. Really the point of the session was an attempt I made at sucking log files down from a server and persisting them on disk in CSV format. Once you have a local static copy you could "perform analysis". Let me warn you, what I have in that presentation is only half-baked. It really is just proof of concept. It needs to be massaged and "made good".
If you want a "more polished" solution, try Trevor Hart's solution which follows the same principals (persist logs locally) into a SQL Database. You then can do some analysis with SQL Server tools or whatever can read a SQL database. I think he's done a great job on it.
So you can see, both approach involve getting a static copy of the logs and then using another tool to do the analysis. One using Python, the other .NET.
(note - there's nothing in the Admin toolkit to provide statistics like this. Just a tool that will show where requests are being made on a map service by generating extent polygons)
We’re reluctant to post anything of a commercial nature here, but we felt it appropriate to round things out (given prior posts) and help paint a complete picture of what’s available.
Latitude Geographics (my role is Product Manager at the company) has a well-established offering in this realm. Geocortex Insight is a licensed product that provides insight into Esri ArcGIS platform implementations.
Drew Millen | Latitude Geographics