Ammonia or rubbing alcohol should cut the spots then use windex to spiff back up the glass.
I don't use Windex anymore. Dollar General stores carry a foam window cleaner. There's other stores that have foam window cleaners also but I don't know your area. Anyhow, the foam cleaners are easier to use and seem to have a higher ammonia content without being smelly. They leave an excellant shine.
I hate spots too. And kid noses :)

I use ammonia and water for nearly all my cleaning and it works great. I remember reading somewhere that baking soda in water makes glass shine, but don't recall the proportions.

I started using the microfiber (I know you know what I mean, for the life of me Im having a small brain fart) cloths..wet, wash the window, (I dont use soap), use a dry one to wipe off...virtually streak free!
(Is it miracle cloths? ) I shouldnt post before coffee :)

Yasmine, considering you posted BEFORE coffee (I'm not brave enough to attempt it), you used the correct word. They are Miracle cloths made of microfiber. And, yes, they are fantastic.

If only I could prevent some others in my house not to use them to check the oil in their car, I'd be much happier. Good thing I get them at the Dollar Store.

I picked up some in the automotive section in the local WalMart and they are way cheaper than a few ailes down in the kitchen towels section! (This is rather like mens clothing costing considerably less to dry clean than womens).
Ive experimented with the miracle cloths, also the magic eraser. Takes off the calcium buildup on pots..also removes stains on the carpets! :) damp a bit and scrub, voila!

2 quarts of water
1/4 cup cornstarch

they're called Sano cloths over here, microfiber anyway you look at it, yep, fantastic. There are mops as well, great for ceramic flooring...

I've heard Coca Cola will remove water spots. Don't want to think about what it does to our insides!

OP's page says s/he lives in California. In the Southwest deserts water spots may be boron in which case glass cleaning products with ammonia are counter productive and mild acids like coke, vinegar and lemon juice may be worthless. If you have boron you need strong acids (Acids which can be dangerous unless you had a good lab in school that taught acid handling techniques.) I would start with lemon juice or commercial white vinegar. If that don't work, and you know acid handling techniques, hydrochloric (muratic) which has real nasty vapors. I had one place in the Nevada desert where I had to go to sulfuric which dissolved all my rags and a cheap toilet brush but it got the boron from the toilet and sink. BTW, old locals may call boron alkali salts. This bit of folk language may help you determine what your problem is.

I use a fine steel wool pad to remove water spots with whatever glass cleaner you want...and no it doesn't scratch the glass...it's what car dealers use on windshields to get the glass sparkling.

I use Stainless Steel Wool #000(must have three zero's or it will scratch. You can use the #0000. Use the steel wool in the packages not the pads itself. Hose off your windows really good with the water hose, then take the steel wool and put some dawn dishsoap on the steel wool and wash the window, ok to put elbow greece on the window, it wont scratch. Hose off window. I have been using this method since 1981. I use it on my cars too. Then if you want, you can use windex or the foam window cleaner. For the inside, if you have film. YOu can use hot water with a tad of ammonia to wash the film off.
Then use windex. clean my windows like this every 3 months. Its relaxing!

Ok...so I have spent hours researching and using many different methods and I finally found this product Ducky Water Spot Remover for Glass and it is awesome. It removed spots that have been in my shower doors, glass tile and windows for years.www.duckyproducts.com

old detailer's trick...Windex or whatever works fine, just use newspaper (black and white, not colored) to wipe dry. Squeaky clean streak and spot free.

Straight organic vinegar on a sponge works great for me in San Diego. We have hard water here.

I had some very intractable marks on the window that forms
part of the shower in the bathroom (it's very private here!). These seemed to be marks and residue left by
water evaporating to leave the calcium and magnesium salts behind, rather than
soap scum from the shower.

Newer deposits on perspex came off easily with white
vinegar, but marks that had been on the glass window for several years would
not budge! I tried: white vinegar, spray
on window and glass cleaner (probably contains some ammonia), tried scrubbing
with a nylon scourer, "Tarn Off" silver cleaner (contains thiourea
and sulfamic acid),caustic dishwasher machine powder, "JIF" cream
cleanser, no-scratch ceramic cooktop scourer with aluminium threads, toothpaste
(two types), oven cleaner (with sodium hydroxide), CLR, hydrochloric acid
(dangerous stuff, do not use unless you have researched what you are doing and
take all necessary precautions) and finally....(drum
roll)...."Gumption" multi-purpose paste cleanser made by Clorox. While the vinegar/acid and glass cleaner
might have made some slight improvement, the ONLY one of these that really
worked was the Gumption. Applied with
the no-scratch glass scourer and a little bit of scrubbing, the windows have
come up brilliantly. At last!

PS I have since noticed very fine scratches on the glass, only visible when the sun is in a certain direction, but there nonetheless. Not sure if they are from the "no scratch" scourer or from an abrasive in the Gumption. This does suggest that it will take an abrasive to remove these deposits and not just a chemical agent alone. 000 steel wool was recommended above.