While asking which layer in the OSI model is the most important may seem akin to asking which part of the body is the most important, the brain, eyes, heart, that is where the analogy ends.
Yes it is true that if there is a problem at the Physical layer, say with a NIC card that no packets may enter the node or network to be processed.
However, if we had to cast a vote as to the single most important layer of the OSI model, it would be Layer 3, the network layer. It is at this layer that routing occurs, and that packets are able to traverse between networks. This is facilitated by the logical addressing that is accomplished by the use of Internet Protocol (IP) which is a Layer 3 protocol.
The network layer is also responsible for packet encapsulation, as well as providing network layer headers for packets. Layer 3 is also responsible for the fragmentation and re-assembly of any packets that exceeds size constraints; this is in addition to the traffic error management that is performed at this layer.
However, the true strong suit of Layer 3 is the host addressing that occurs via the logical addressing performed by the Internet Protocol, as opposed to the physical addressing executed by Layer 2 the Data link layer and the routing implemented by OSPF, BGP, RIP, CDP, IGRP, and other routing protocols.
Layer 3 protocols and technologies allow for network-to-network communications. In the Open Systems Interconnection (OSI) communications model, the Network layer knows the address of the neighboring nodes in the network, thus packages are output with the correct network address information, and route selection and quality of service (QoS) is facilitated.
So much of what we do as network administrators, working with QoS, IP addresses, sub-netting, routing protocols, firewall rules and Access Control Lists (ACLs), is enabled by Layer 3 technologies. When troubleshooting network issues, it is helpful to understand if the issue is occurring at Layer 2 or Layer 3 of the OSI model. If you're able to get local communications to work but the packets aren't traversing your Layer 3 boundaries then you've got a Layer 3 issue on your hands.
The reader is also cautioned to keep this in mind when working with a Layer 3 switch, is simply a Layer 2 device that also does routing, a Layer 3 function. Another significant aspect of routers to keep in mind is that each interface on a router has its own IP address, because each of those interfaces is on a different network.
Nonetheless, when troubleshooting Layer 3 issues, an understanding of Layer 2 technologies can sometimes be a huge help. For instance, if you can't get communications from one side of a router to the distant side of an adjacent router, checking for Layer 2 connectivity with say the Cisco Discovery Protocol (CDP) between the two devices may provide us with great insight into the problem.