I used to make cinnamon vodka. Get some Chinese cassia cinnamon (paying for the good stuff is totally worth it in this case–the 4 oz. bag will be enough for several bottles) and put a few tablespoons of it into the vodka along with the resin from the inside of a vanilla bean or two. Add just a touch of cloves and nutmeg. Let it sit in the fridge for a week or so, then taste it and see if you like it. If you do, strain it through a colander lined with coffee filters.
It’s absolutely delicious, but surprisingly (to me), it didn’t really mix with anything. I liked it best as an ice-cold after-dinner shot, kind of a dessert for those who prefer booze to sweets.
My sister usually has a bottle of lemon-infused everclear which she makes for parties. Don’t know why she uses Everclear, but it’s tasty.
There are commercial vodkas infused with jalapeno, which has a wonderfully grassy taste, not too hot, tastes just like you’d expect. Rather good. Another one I tried recently is infused with wasabi – that’s a rough drink, IMO, straight up, but tastes good mixed with OJ. I don’t see why you couldn’t make something like that at home.
My dad was doing this in the early 60s. He had had Strega in Italy and couldn’t find it back home except at a horrendous markup, so he experimented with infusing lemons, herbs, and sugar in vodka. He says he never quite got the flavors to balance right.