Question: I am trying to sniff packets using Wireshark.
But Wireshark collects packets of computers connected to my Router only.
If i know the IP address of a Computer , can i sniff the packets of that Computer ?
Or is there any way to sniff packets of Computers/devices that are not connected to my Router ?

Answer: 
Wireshark can collect packets on any interface that has those packets passing it. 

1. If you are running wireshark on a PC etc, then you will collect data from the machine it is running on to any other machine on the network.
2. If there is a hub in between that machine and any other machine you will see all of its traffic also. (hubs rarely exist in networking any more - unfortunately!)
3. If there is a switch between you and the other machine, you will only see broadcast traffic from the other machine. (if it is a managed switch, you can 'mirror' a port to allow wireshark to 'see' all the packets travelling across that port.
4. If you are running wireshark on a router, you will see all traffic passing over the interface that you have wireshark listening on. i.e. if you have a three port router, with lan1, lan2 and wan and listen on lan1, you will not see traffic going lan2 <> wan. but will see lan1 <> lan2 and lan1 <> wan1
5. If lan1 (as #4) is connected to a switch (as #3), the same will apply as #3
Your network is most likely switched. That means that (except for some initial traffic) unicast packets only take the most direct router from source to destination. This means you have to be a man in the middle to capture traffic. You’re currently running on the router, that means you have access to all non-internal communication.

The [Wireshark wiki](https://wiki.wireshark.org/CaptureSetup/Ethernet#Switched_Ethernet) has a great page on why capturing packets in switched networks is very difficult. The easiest method is to run a [MITM attack](https://wiki.wireshark.org/CaptureSetup/Ethernet#Capture_using_a_MITM_.28Man-In-The-Middle.29_software) against computers in your network using ARP poisoning:

> 
> This type of attack will fool the two computers into thinking that your MAC address is the MAC address of the other machine. This will in turn make the switch route all of their traffic to your computer where you can sniff it and then send the traffic along as if nothing ever happened.
> 
> 
> 

So yes, if you have a specific IP address you can indeed use this attack. However, doing so outside your home network is not advisable and even illegal in some countries.