On a consumer level, weather instuments as an aid in the garden and landscaping are generally just basic. For the average home gardener, the most common instruments are a simple rain guage and a thermometer. Once in a while I may see a Barrometer, wind chill, and wind direction meter. Other than that, most gardeners are just fine without them.
As you get into cash, seed, plant propagation, and agricultural crops, the need for sophysticated weather instruments is quite obvious. A controled atmosphere and fewer surprises from nature are very important for keeping track of what makes garden plants grow in certain ways. So this is where you'll see the most use of weather instruments in the garden.