This curiosity started with port 80. I know that a web server program listens to port 80 where most http traffic comes into the system. (This setting is by default). Even browsers sends/receives http traffic if I am not mistaken. So shouldn't they technically use port 80 for communicating?

If this is the case if you have both a web server and a browser program, how does the browser only receive traffic/data corresponding to the requests it has created...?

There's a difference between client port and server port. HTTP servers bind to and listen on port 80. HTTP clients bind to a random high-numbered port on their side before connecting it to the server on port 80.

Suppose a client browser sends a http request to a server @ www.example.org, then we should be technically able to see the port number the client has used to send the HTTP request written to the server logs (@ example.org) right?

netstat
will give you a clue.

of interest to you, if you have netcat installed.

type
and then type "get".

or be a web server,

(it may be nc -lp depending on the version)

and put localhost:50123 in your browser.

HTTP protocol sits on top of TCP/IP, and in the latter packets have source and destination address, i.e. both participants of the WEB conversation know whom they are talking to.

You might want to take a look at the wireshark tool. It shows all of the packets within a transaction. Unfortunately, if you have other activity going on the computer it will pick those up as well so you will need to learn how to filter the results. I just ran a quick session to pull up the Google home page and there were about 250 packets. Most of those I'm not interested in so since you know that port 80 is the port of interest you can search for that using a filter:
However a possible better approach would be to start at the beginning and find the DNS packets. For that I used a filter:
The results from the DNS query tell me that it will establish a link with the server with IP address of 74.125.71.147 With that little piece of knowledge I can set up a filter to look at just the packets sent to that address.
From these packets displayed I can see what happens before my browser gets anything to display from the web server.

The first three packets are important and for what is known as the three way handshake. My browser sends an synchronise packet [SYN] which tells the web server to respond to me using this IP address and this port - in this case port 50021. The second packet comes from the server and Acknowledges the first packet and asks for acknowledgement in return [SYN, ACK]. The third packet acknowledges [ACK]the servers packet and a connection has been established.

What follows this is the request from the browser and the response from the server.

That's helpful graemef

So it is the choice of a different port (in this case 50021) that enables both participants to uniquely identify TCP packets as belonging to a specific connection. There may be many such uniquely identifiable TCP connections between the same two participant computers.

This text, from Wikipedia, sums it up nicely: "Arriving TCP data packets are identified as belonging to a specific TCP connection by its sockets, that is, the combination of source host address, source port, destination host address, and destination port. This means that a server computer can provide several clients with several services simultaneously, as long as a client takes care of initiating any simultaneous connections to one destination port from different source ports".

moved to General

Neither a Linux nor a Programming question this is....