There are a huge number of cocktail recipes that, being allergic to juniper, I've never been able to try because they contain gin. I know that juniper is a fairly distinctive flavor and gin won't be easy to substitute for, but I'm hoping there is some non-juniper-containing liquor which may be "close enough."
I'm not sure if you just want to be able to make the recipes, or if you also want to have the juniper taste without the allergic reaction so to speak. Finding a substitute shouldn't be too hard, but they won't quite have the same taste. Vodka is suggested for martini-type drinks:
This is a tough one to pull off, but in general, if you are making martini-type drinks, gin can sometimes be substituted for vodka, and vice versa. While these alcohols taste quite different, the texture and appearance of a cocktail is not altered by switching, and can often be just as good.
I came across a video on making something gin-like out of vodka, but it says “juniper berries are the key ingredient.” Perhaps you could still add the cardamom and other spices to match the gin flavor more closely though. Here's another page with similar instructions (check the page for the recipe):
But what many people don’t realize is that gin and vodka begin life in the exact same way. You could even say that gin is nothing more than infused vodka. [...] In his book The Complete Guide to Spirits (HarperCollins, 2004), Anthony Dias Blue describes cold compounding as a legitimate method for producing gin.
For other types of drinks, Cook's Thesaurus lists a few other possible substitutions:
gin This is distilled from grains and similar to vodka except that it's flavored with juniper berries, herbs, peels, and spices. London gin = dry gin = English gin = London dry gin is the preferred gin for martinis and other mixed drinks. American gin is similar, but isn't quite as heavy and dry as London gin. Hollands gin = sweet gin = Dutch gin = Geneva gin = Jenever is sweeter and more aromatic than other gins and isn't normally used for mixed drinks. Tanqueray and Beefeater are well-respected brands. Don't confuse gin with sloe gin, which is sweetened.
Substitutes: vodka (This turns a martini into a vodka martini, a gimlet into a vodka gimlet, a gin and tonic into a vodka and tonic, a Tom Collins into a vodka Collins, and so forth.) OR white rum OR whiskey OR tequila OR brandy (This turns an Alexander into a Brandy Alexander.)
As was said in previous answer, gin is basically infused vodka, and there's lots of different gin recipes. But as a replacement for juniper I would try something piney with bitterness. Rosemary and certain varieties of hops (used in beer) come to mind. Both are very easy to get your hands on, as hops are sold in any good homebrew store. There are also citrusy varieties of hops, so you'd want to experiment and do some research if going that route (hops chart). Bay leaves might also work.
Rosemary or hops infused vodka won't be all the way there though, as gin again, may have many other flavorings. From Wikipedia:
"London Dry gin is usually distilled in the presence of accenting citrus elements, such as lemon and bitter orange peel, as well as a subtle combination of other spices, including any of anise, angelica root and seed, orris root, licorice root, cinnamon, almond, cubeb, savory, lime peel, grapefruit peel, dragon eye, saffron, baobab, frankincense, coriander, grains of paradise, nutmeg and cassia bark."
Hendrick's gin adds rose and cucumber. If you look areound there are countless other recipes you can find on homedistilling, homebrewing and mixology sites.