There's countless websites that do this type of thing in one form or another. Personally I've never found one that does exactly what I want, but for the most part the following 2 sites do something similar to part of what you've described.
TripIt is a great travel planning site. It allows you to forward confirmation emails from hundreds of different travel booking sites, and it will automatically merge the details into a single "trip" listing all the details you've sent it (flights, hotels, rental cars, etc), along with location information for the places you're going like maps, weather, etc. In the unlikely case that it can't understand the email that you've sent it - or if you want to enter additional information (meetings, other plans, attractions to visit, etc) - then you can just enter these items manually via the website.
There's an app for a few different platforms that you can use to access your trips, and there's also the ability to share your trips with others, and even see which of your friends you'll be near during your travels (presuming they are also using TripIt, obviously).
TripIt does have some statistics after the trip, but in order to track where I've been I enter my flight details into FlightMemory. Once you've entered the flights, this site will give you maps showing where you've been, as well as details of the number of miles you've flown, etc. There are other sites out there that potentially do the same thing with a little more updated user interface, but I've been using Flight Memory for years, and it does the job well.
Personally I'd love to find a cross between TripIt, FlightMemory, and something like EveryTrail - but if it's out there I've yet to find it!