Well, there are a bunch of choices. And I don't know which is best for you. But I'll present them here with some pros and cons and you can come to your own conclusions given your requirements.
The simplest answer is "put it in storage." Both SQL Azure and the core Azure table or blog storage options are out there for you. One issue to contend with is performance in the face of large scale concurrency, but I'd also encourage you to think about correctness. You really want something that supports atomic increment to outsource this problem IMO.
Another variation of a storage oriented option would be a highly available VM. You could spin up your own VM on Azure, back a data drive on to Azure Drives, and then use something on top of the OS to do this (a database server, an app that uses the file system directly, whatever). This would be more similar to what you'd do at home but would have fairly unfortunate trade-offs...your entire cloud is now reliant on the availability of this one VM, cost is something to think about, scalability of the solution, and so on.
Splunk is also an option to consider, if you look at VMs.
As an earlier commenter mentioned, you could compute off of log data. But this would likely not be super real time.
Service Bus is another option to consider. You could pump messages over SB for these events and have a consumer that reads them and emits a "summary." There are a bunch of design patterns to consider if you look at this. The SB stack is pretty well documented. Another interesting element of SB is that you might be able to trade off 100% correctness for perf/scale/cost. This might be a worthy trade-off for you depending upon your goals.
Azure also exposes queues which might be a fit. I'll admit I think SB is probably a better fit but it is worth looking at both if you are going down this path.
Sorry I don't have a silver bullet but I hope this helps.