I have an 11yo and a 7 yo.
My kids dont really have an allowance at this time. I do have an amount in my budget set for activities and for toys/games/apps/ etc (usually 25$ a month for each of those categories). what we spend comes out of those categories.
IMO, there are different kinds of "I wants".
There are the impulse ones-like walking thru Target and any thing they see that is interesting...or watching a commercial etc. I deal with those by first, acknowledging and repeating. "ooh, thats cool!" or "yeah! look at that!" or even "oh, you like that". Often, I offer to take a picture of the item for them. Or of them holding the item. Sometimes they like this idea. This was more satisfying to them when they were younger. I will also offer to add it to their Wishlist. I used to just write it down on a pad of paper. Then we had a whiteboard. Now, I have made them wishlists on amazon. my daughter can add stuff to her own now, but I still add stuff for my son all the time. His wishlist is several pages long.
Most of the time I dont have to actually say no-they usually understand what my response to the "I want" is going to be. I have been doing this a long time :) I often have similar feelings in the store. I dont want to shame them about what they want, or give a lecture, or be depressing about how we dont have money for it. I wouldnt want anyone to do that to me. And, my kids know that even if they do get something, Im going to research the best price anyway before deciding. we rarely do the impulse toys buys.
for food items, Im flexible. It depends on how much I have in the budget. I do get treats sometimes. Last year, mcdonalds had ice cream cones for 50c all summer. We stopped there a lot just for ice creams. It was fun, and pretty cheap. Guys at the parks sell ice cream novelties for 3$ each. this was my compromise. I also make a lot of treats. I did homemade milano cookies for a fun thing once. etc.
Then there are things that make it past the impulse test and stand the test of time. that is, they are still asking about it several more times.
If they have their own money, they can use it how they want.
If they are out of money, I will see if there is a way to borrow, buy used, etc before I consider buying it new, but then find the best price.
I often say "Im not going to buy it right now, lets research it" but then I follow thru on that, otherwise it wont keep "working" as in, the kids will understand its a put off.
I will say that there was about 18 mos where I would not even DRIVE BY a target, because my son would just desperate to go in there and buy CARS and Toy Story stuff. nothing would distract him or console him. He was 3 ish when it started. Even driving by would make him cry and beg to go in. So I literally took another route to avoid it. Dont make things worse for yourself! :) If shopping without buying is really hard for your kid, avoid it for time being. Now mine is ok to go to target, although we almost always just go and look at the toy aisles, but they know its just for looking.
I also "prep" them when entering a store. I say what we are looking for, planning to buy, ask them to help in various ways, get them involved. They know going in we arent going off list. Sometimes I say, you can each choose something that is 5$ or less.
Sometimes if the situation is getting tense, I have a technique I call the Magic Tree. Kids says, "I want x". I say:" what if you had a magic tree that could grow anything you want? Would your tree grow X? Mine would grow.... chocolate!" I try to diffuse and change the conversation. "what would Daddy's tree grow? maybe....bowls of chicken soup! thats his favorite!" make it silly. Or I just start being goofy and listing all the things I "want"...oh, you want the disney princess game? I want...summer weather! I want....a clean bathroom! I want...a big bowl of ice cream. What else do you want?" The key is to keep it light and silly. I cannot tell you how many power struggles and tantrums I have squeezed out of with this technique (inspired by Playful Parenting by Lawrence J Cohen)