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The command used to check connectivity to a remote host is 'ping [hostname]'. When you use the ping command, it sends Internet Control Message Protocol (ICMP) Echo Request packets to the specified hostname or IP address. If the destination is reachable, it responds with ICMP Echo Reply packets. This allows you to determine whether the remote host is accessible over the network and can also provide information about the round-trip time for the packets sent.

The ping command is a fundamental part of network diagnostics and is widely used by system administrators to troubleshoot network issues and ensure that devices can communicate within a network. It is simple to use and provides immediate feedback, making it an essential tool in system administration.

Other commands listed do not serve this purpose. For example, trace may imply trying to track the route taken by packets, but it is not a standard command and might be misunderstood in this context. Similarly, check and connect commands are not standard network utility commands in Linux for testing connectivity. Thus, 'ping [hostname]' is the correct and widely recognized choice for checking the connectivity to a remote host.