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:
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):
For other types of drinks, Cook's Thesaurus lists a few other possible substitutions:
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.