While the point of frugality is usually to avoid spending money, there are some good frugal tool investments that are worth spending on, because they really do save you money in the long run. Of course, I'm going to recommend that you pick up as many of these items second-hand as possible. Many tools are just as good used as brand new.
For any number of kitchen applications, rubber spatulas are a frugalite's friend. Spatulas help you get an extra few tablespoons of sauce, the last of that soup, and an extra muffin's worth of batter. A good rubber spatula will last for years and help you waste not, want not in the kitchen. I like the Kitchen Aid spatula. I have a couple of these in my kitchen.
A food processor is a great frugal kitchen tool, provided that it actually gets used on a regular basis. This tool can mean the difference between tiresome drudgery and quick preparation time for many foods. I most often use my food processor to grate large blocks of cheese so that they can be frozen to use on homemade pizza at a later date. True, I could get out my hand grater and do it all with elbow grease, thereby saving a few pennies in electricity. But if I knew that I'd have to grate it all by hand, I'd be much less likely to stock up on cheese when I found a good deal. The same goes for preparing large batches of morning glory muffins. Grating a couple pounds of carrots and apples takes seconds rather than half an hour with a food processor. So this is a tool that helps and encourages me to make good frugal choices in both shopping and cooking. Some bakers also use a food processor to knead their dough. I sometimes use mine to puree sauces and soups. You don't need a very fancy food processor, nor a new one, to get good results. For those making a real commitment to a frugal lifestyle, I think a food processor is a worthwhile investment.
A Chest freezer is a great thing to have in the basement or in the garage. If you own your home and have the space, think seriously about investing in a freezer. It will allow you to stock up on all sorts of food when there's a good sale, or when produce is in season. This is one item that you should probably buy new. Chest freezers are more efficient than other kinds of freezers for one very simple reason. The cold air won't spill out of them when you open the door. And the efficiency of freezers has improved so much over the years that you will quickly recoup your costs for a new freezer as compared with an old one by virtue of the lower electrical bill. Look for the EnergyStar label as you do your shopping research.
Durable, re-usable food containers - these are essential items for any frugal home. Use them to store leftovers and to pack lunches for work or school. They are sturdier and more cost-effective than disposable plastic bags. They come in a variety of shapes to suit sandwiches, fruits and vegetables, and even soups. Ziploc brand has some good screw-top lid containers that I've used to pack soup in checked luggage on an airplane. I've never had a spill with these, though I continue to double bag them. The brand is much less important than having a plentiful supply of these around. You can even save yogurt containers and the like to use for leftovers. Just don't forget what's in those opaque containers. If you tend to the out-of-sight, out-of-mind school of leftover management, as I do, it may be better to store your food in clear plastic containers or bags - even if you have to pay for those containers.
Other basic kitchen tools are needed to do any serious amount of cooking. And cooking is one of the irreplaceable frugal skills. So make sure that your kitchen contains a working version of a colander, paring knife, chef's knife, wooden spoons, chopping board, mixing bowls, measuring cups and spoons, and a set of good-quality cooking pots. Without these and other staples of the kitchen countertop, you'll be hard pressed to prepare your meals at home. Going without basic kitchen tools is a false economy if you end up ordering takeout because you can't face the task of preparing a thrifty meal in a frustratingly under-equipped kitchen.
No household should be without basic hardware tools. Whether you rent or own your home, you'll eventually need a hammer, screwdriver, wrench, measuring tape and probably a wrench and a pair of pliers. Sears Craftsman tools are guaranteed forever, and can often be found at garage sales. I remember a story about a young woman who was given a basic set of Craftsman tools by her practical father when she went off to college. Before he gave them to her, he painted all of them pink. She objected mildly to this, because she wasn't exactly a girly girl sort. Her father reassured her that the color was not a means of accessorizing, nor feminizing the tools. Instead, it was insurance that she'd always have her tools returned to her when they were borrowed, especially by men. Sure enough, not one of her tools ever disappeared after being borrowed. Many years later, she still had the same set.
I'm going to go ahead and recommend a hot glue gun, even though I'm somewhat on the fence about this tool. I haven't had mine all that long, but I have gotten a good amount of use out of it. I don't do a lot of crafts. I suspect that crafty sorts and parents who like to keep their kids busy with creative projects would find this tool enormously useful. I find mine great for a myriad simple repair jobs and the few crafts projects I've tackled. If this tool makes sense in your frugal life, then by all means pick one up.
A hot water bottle is your friend if you live where the winters are cold. A good frugal housekeeper knows that it's cheaper to keep a small spot warm than to heat a whole house. If you have time during the day when you have to sit still for hours on end (homework, writing, research), you know how hard it can be to stay warm in a house with the thermostat set to 63 degrees. Invest in a hot water bottle for each family member. Make simple cloth covers for each one out of old clothes or an old comforter. The covers keep the bottle hot longer, and also help keep you from getting burned on the hot surface. When your water bottle wears out, it makes a good kneeling pad for garden work. It'll keep your pants cleaner and you can put a little sand in it to cushion your knees.