Is it possible to see personal Facebook usage statistics from facebook.com or some other web service? By statistics, I mean, for example, the total number of likes, posts, logins, etc. (maybe detailed in periods).
I think that the best option is Wolfram Alpha.
Check it out at http://www.wolframalpha.com/input/?i=facebook%20report
Klout.com offers, as part of its measurement of how "influential" you are online, some Facebook stats such as # of likes and comments (total / per post).
Disclaimer: Klout is quite limited with regards to Facebook (being more Twitter-oriented), and it seems a Twitter account is required to be able to use it at all.
(But at least Klout proves that some such statistics are indeed available through Facebook's APIs, so quite possibly there are other services that provide what you ask for...)
As all of those apps no longer work but here is a new Facebook app: "Facebook Analytics"
It will give you all those answers and more in a very user friendly way. It also works for pages. Here is the description from the page:
A free tool for analysing your Facebook data. Use Analytics to know:
The total number of likes, comments and shares
Who comments and likes the most
Which users get the most likes and comments
Who the most influential users are
Which content generates the most interest
Who are the most influential users outside of your social circle