Everyone knows you need to keep your makeup brushes clean (how often you actually clean them is another story), but it's the other makeup tools we use that slip through the cracks of cleanliness. I thought about this when I was looking for scissors to cut a hydrocolloid bandage with; I clean the ones in my makeup kit for every job, but my personal ones don't always get the same attention.
Whether or not you abide by the six-month use-by rule on mascaras, you'll at least understand the reasoning: eyes are delicate and eye infections are gross. Eyelash curlers don't have the same moist environment that the inside of a mascara tube does, but they still make contact with the base of your lashes daily. Do yourself a favor and keep them clean with a thorough wipe-down of isopropyl alcohol regularly — and when the rubber pad starts breaking down, replace it right away.
Lash curlers are a single-purpose tool, but tweezers are the everyman of beauty tools and can cross-contaminate from all over. I can't be the only one who uses the same pair of tweezers to pluck my eyebrows, apply false lashes and have the occasional dig at an ingrown hair. Again, your pair of tweezers will benefit from a dose of iso. Alternatively you can toss 'em in a pan of boiling water for five minutes.
Like tweezers, pencil sharpeners tend to come into contact with products that touch your eyes and lips, and they might not always get a clean in between each one. Anything that's going near your waterline, in particular, should only be sharpened with a clean pencil sharpener. You can throw them into the pan with your tweezers when you boil them, and scrub them with a toothbrush to get all the product build-up out.
Cuticle pushers and other nail tools also fall into this category. You'd want your nail salon to be maintaining impeccable cleanliness, and you should treat your own tools with the same expectations. The nails themselves might technically be dead, but tiny cuts and hangnails give plenty of opportunity for germs to get in. As before, give them a thorough boil or wipe down with iso.
Hot tools get product built up on them more than anything else, but they'll still work a whole lot better when they're clean. Keep these ones well away from running water! I often give the plates of my straightener or barrel of a curling wand a swipe down with my towel before using them, but it's good to give them a thorough wipe down with isopropyl alcohol once a month or so (more if you use them daily).
Most of these devices claim to have antibacterial bristles, but after they've been used a bunch of times the bristles can start breaking down and getting little cracks in them, which are perfect spots for germs to lodge themselves. Obviously they tell you to replace the brush heads regularly anyway, but you should probably give them more than a cursory rinse after each use. Work some cleanser into the bristles with water as hot as you can handle, and make sure they dry quickly. (Maybe don't store your Clarisonic in the steamy bathroom, either.)
This one I've learned from experience: sharing brushes without sanitizing them is bad, but even your own hairbrushes can get nasty if you don't clean them regularly. Professionals use Barbicide, which you can buy from a salon supply store, but you can give them almost as thorough a clean without any special products. Pull as much hair as you can out from amongst the bristles. I find a bobby pin helps, or you can run a comb along the gaps between the bristles. This is therapeutic but also kinda gross.
After all the hair is out, you can boil the brush, but if it's got plastic parts or if it's your nice Mason Pearson, you probably don't want to. Give it a good shampoo by hand in hot water and use a toothbrush to get right into the gross corners. Leave it to dry somewhere it will dry fast (this part is hard in the winter in my house). Sometimes I give my brushes a spritz with tea-tree oil as an additional anti-bacterial measure.
A note on isopropyl alcohol
Isopropyl alcohol is not the most effective disinfectant that exists, but it does strike the balance between effectiveness and safety for home use (as opposed to, like, a hospital). It seems like there's always debate about what strength to use, but it's generally recommended to use around a 70% solution for cleaning makeup brushes and disinfecting beauty tools. Using a higher percentage puts the alcohol at risk of evaporating before it can actually do anything.