If you can find it near you (or order online): 3M's SS Cleaner and Polish aerosol spray works well (thank you once again to rococogurl for the suggestion--we also use it on our KA fridge). Spray it on a cloth or micro fiber cloth, wipe on (covering all SS surfaces), and then buff in/off with dry part of the cloth, or a fresh cloth. It's approved by the NSF as being safe to use around food, and I use it on my SS sink a few times a week to repel or cut down on water spotting.

For scrubbing off "gook" and cooked on food, you can use some BKF (Bar Keepers Friend) on a blue scrub sponge, and then remove powdery residue with wet/damp sponge or paper towel, and then follow up with the SS spray.

I have a Jenn Air pro style range and generally just use soapy water and and occasionally a little BKF. I use only microfiber cloths on all my stainless appliances and it works great - no additional chemicals or cleaners needed.

I am waiting for the skins on my ss fridge to be replaced, so I have taken advantage of trying different suggestions on my soon to be ex-fridge door skins. It was suggested by some GW'ers to use WD-40. Sray a little on a microfiber cloth wipe it on the surface and then wipe it off. Oh My Goodness--it works great! And so easy..

Another item that comes highly recommended is Sheila Shine. Somewhat expensive, but if you just re-use the same cloth (keep it in plastic bag between uses) the product seems to last years.

Here is a link that might be useful: sheila shine

I use either Pledge in the brown can or Weiman SS cleaner/polish spray (not the wipes). Both work great...they easily & quickly remove fingerprints and seem to make my appliances resistant to new fingerprints.

The old "clean as you go" still works. Cleaning as soon as you see smudges and dirt is inexpensive in the long run. I also use Pledge. Works for me. :)

I find that what you use is totally dependent on the specific type of stainless steel you are dealing with.(There are many different grades.)With my old Wolf AG range and hood, Stainless Steel Magic worked great. On my Liebherr, it doesn't work at all. The Neoblank(petroleum based) liquid that came with it does an OK job, but always seem to get some kind of streaking. Meyer's Stainless works great on my Miele oven, and on my Sharp Stainless Microwave I can use just about anything. Frankly, it's all rather annoying.

Thank you, everyone, for all of your advice and suggestions! I now have about a dozen different products to try.
:)

I have stainless counters and appliances. On both, I first go over everything with a hot, wet microfiber cloth, then a dry one. Usually, that takes care of all the smudges and finger marks. Once a week, or once every other week I use the 3M spray.

As for the WD-40 -- the can gives warnings that it's flammable, harmful or fatal if swallowed, a breathing hazard, and not to touch your skin. I would never use that in a kitchen. It's not meant for cleaning.