Lawr1165:
If .38 S&W Special, then you have a .38 Military & Police Postwar (pre-model 10) manufactured in 1953.
If .38 S&W (not special) then you have a .38/200 Military & Police. These were mainly for sale in the British Empire.
If .38 S&W Special but with an alloy frame (try a magnet) then it is a .38 Military & Police Airweight. These have an KA aluminum frame which is slightly narrower than the steel K frame and aftermarket grips may not fit.
If an airweight and the cylinder is also aluminum it should not be shot, instead find a collector willing to buy it and buy two shootable guns with the money.
thomaskm:
If original then the grips are probably real ivory or mother of pearl and may be worth as much as or more than the gun. Start a new thread with pics if you want them evaluated.
The grip safety & serial number indicate you have a .32 Safety Hammerless 3rd Model, often called a lemon squeezer or New Departure. Yours was manufactured between 1909 (serial number 170000) & 1915 (serial number 205477). Based on roughly 6000 guns a year, 1910 seems likely.
Your gun should be safe to shoot with modern factory ammo, S&W started advertising these as safe for smokeless powder around 1906/7.
These guns definitely had a trigger guard.
http://www.gunpartscorp.com/catalog/Products.aspx?catid=8049 has them for sale.
Workhorse:
Your Model 19-3 Combat Magnum was manufactured in 1975.
walkindude:
Your Model 686 Distinguished Combat Magnum Stainless was manufactured in late 1984. There is a recall on this model. With some magnum ammo the primer can flow back into the firing pin bushing, locking up the gun. Under the recall S&W will pay shipping both ways and install an new firing pin and bushing. If your gun has been modified there will be an M stamp near the model number under the crane. If not, and you want to have the gun modified, call S&W and they will send you a shipping label.