Yes, you can see all the packets that arrive at your network interface. There are several options to access or view them. Here a small list of possible solutions, where the first one is the easiest and the last one the hardest to utilize:
Wireshark
I'd say this is pretty much the standard when it comes to protocol analyzers with a GUI (uses libpcap). It has tons of options, a nice GUI, great filtering capabilities and reassembles IP datagrams. It uses libpcap and can also show the raw ethernet frame data. For example it allows you to see layer 2 packets like ARP. Furthermore you can capture the complete data arriving at your network interface in a file that can later be analyzed (also in Wireshark).
tcpdump
Very powerful, similar features like Wireshark but a command line utility, which also uses libpcap. Can also capture/dump the complete interface traffic to a file. You can view the dumped data in Wireshark since the format is compatible.
ngrep
This is known as the "network grep" and is similar to tcpdump but supports regular expressions (regex) to filter the payload data. It allows to save captured data in the file format supported by Wireshark and tcpdump (also uses libpcap).
libnids
Quotation from the official git repository:
"Libnids is a library that provides a functionality of one of NIDS
(Network Intrusion Detection System) components, namely E-component. It means
that libnids code watches all local network traffic [...] and provides convenient information on them to
analyzing modules of NIDS. Libnids performs:
- assembly of TCP segments into TCP streams
- IP defragmentation
- TCP port scan detection"
libpcap
Of course you can also write your own programs by using the library directly. Needless to say, this requires more efforts.
Raw or Packet Sockets
In case you want to do all the dirty work yourself, this is the low level option, which of course also allows you to do everything you want. The tools listed above use them as a common basis. Raw sockets operate on OSI layer 3 and packet sockets on layer 2.
Note: This is not meant to be a complete list of available tools or options. I'm sure there are much more but these are the most common ones I can think of.
IP Fragmentation
in tcpdump man page. – viraptor