I need to trace/sniff http traffic from other machines (for example from my android phone or ios device). In the past I used MSSOAPT (described here http://www.devproconnection
Look at charle proxy it is very easy to use and has all your requirements fulfilled.
If you are on Windows, Fiddler as a great free tool.
On other platforms, you could use the free and open-source WebScarab. The UI is not as easy to use as Fiddler, and although it runs on Windows, I rather prefer Fiddler there.