If you have not firewalls and routers in the way, i.e., if you're on the same segment as the host you're trying to check - most of the solutions above are a little exhaustive imho.
It doesn't matter what port you connect to, and in fact, if you connect to a port that's unlikely to have a service running, you can get the job done without being detected.
You can use any tool you like, but we can just use telnet...
% telnet <host> 313373
telnet: connect to address 10.211.55.3: Connection refused
telnet: Unable to connect to remote host
This should happen immediately, unless the host is dropping packets. What's actually happening is that the TCP/IP stack on the host is sending you back a TCP segment with the RST bit set - i.e. terminating your SYN packet.
The fact that you received a RST packet means that there is indeed a host up at the other end, and as a bonus - you've done so undetected (The TCP/IP had no upper-layer application to talk to about this connection).
Rather than telnet however, I'd probably use something like scapy, write up something that looks for the RST flag and let's you know.
Just to complete this, if there is no host on the IP that you try - it will hang for a little while, and the timeout - the same thing that would happen if the receiving host had a firewall with a drop filter.
If firewalls are involved, then as others have suggested, make use of tools such as
nmap and whatever else.