As others have pointed out, you can ssh into a remote system without having to type a password every time by using ssh keys (google for "putty ssh keys" to find a lot of tutorials).
However, if your intent is to monitor a remote system, I think you're asking the wrong question. If you want to know the uptime, load, and other useful stats about a UNIX machine there are a couple of choices:
The former (SNMP) is a simple protocol (as the name suggests) used to monitor network devices, printers, UPS systems, and the like. I bet even your home router supports SNMP queries. A SNMP monitoring tool just sends queries over the network and parses the data it receives.
The latter (Nagios) is a framework with monitoring capabilities for various aspects of remote servers such as disk load, application status, performance, and so on. It can use SNMP and overall does quite complex tasks such as making sure a web server is still responding to a specific request, that a SMTP server is working, that a network share is not full, etc. It's a bit cumbersome to set up the first time but if you have a large infrastructure it's a must.