what are some ways to tell SQL is alive remotely?

I am trying to set up some remote monitoring code so that I can monitor whether or not SQL Server is up and running properly. What are some good stats to check (the fewer the better) to give a good feel of whether or not SQL is behaving and is active and alive on the servers it is on? I'd
like to check and get stats for things like availability, throughput, response time, and if it is up and running at all. Any suggestions as to what the best things to monitor are?

Jacob Yackenovich
Senior - Computer Engineering
The Ohio State University