I don't have the best equipped kitchen in the world. I have what I was able to steal from my old apartment (my brother still lives there), what I was given by my parents and friends before moving, wedding presents, and a few things we bought after we moved. That sounds like a lot, but we really have a sort of random assortment of things.
I don't have any 8x8 or 9x9 inch square baking pans. Instead I use a 13x9 lined with aluminum foil to make it the right size. It's not pretty, but it does the job. The foil also makes clean up easier!
I don't have a mesh strainer. I want one, but in the meantime I can deal with it. I have a big colander that I can line with paper towels or clean kitchen towels for straining liquids. I have a small holed cheese grater that I can use for things that don't need to be as fine. I want a mesh strainer for sprinkling powdered sugar, but I haven't needed to do that yet.
Those are the only clever substitutions I've come up with so far.
Some things I wouldn't want to live without:
My kitchen aid stand mixer. It makes cakes super easy. I wouldn't want to make icing without it. I also used it for mixing yams on thanksgiving. I use it about once every two weeks, but I think it deserves a permanent place on my counter. I like it better than a hand mixer because I can use it for bread (if I ever make any) and I can leave it running without having to hold it. I can have it whip egg whites or cream while I work on something else. Hand mixers are alway too heavy for me and I don't have the patience to make whipped cream with them.
A big pasta pot with a colander insert thing for easy draining. I don't know what it's technically called. Making pasta is super easy and I don't have to lug a pot of boiling water to the sink and then try to get it all in the colander. This is much easier for me. I also used it when making broth. I put all of the vegetables in the insert and then just pulled it out when it was finished. I didn't have to fish everything out or deal with big cheesecloth bags or any of that hassle. Then I put the broth into a big pitcher for easy access during Thanksgiving.
An immersion blender. My mom just bought one for us, so I lived without it for a while. (She bought us a red one that matches our kitchen aid!) I prefer a hand blender to a countertop one. I like being able to blend a smoothie right in the cup I'll drink it out of. I've also had bad luck transferring boiling soup into a blender and then into another pot. This requires less pouring of boiling liquid (always something I avoid) and less clean up. I don't have to clean two pots and the blender. I just clean one pot and the hand blender. I love anything that requires less clean up.