There are obviously many items that do not fit into any of the above categories.
Eggs. Many cocktails call for egg white. Almost all salmonella is contained in the yolk so, unless you’re severely immunocompromised, it is generally safe to use the white in cocktails for substance. I don’t make flips, which call for the whole egg, as it’s not worth the risk in my mind. Ideally, eggs for mixing should be brought to room temperature. In fact, I’ve done a lot of traveling and have found that it is only in western world where eggs are kept in the refrigerator.
Taiko Demerara Sugar Cubes. I use these exclusively in my Old Fashioneds and Sazeracs.
Rose Water. I own a bottle of this beautiful stuff but barely ever use it. Same goes for hibiscus water and jasmine. Some of the old recipes call for rose water.
Cream. I always have 10-15% cream on hand in the summer when making tropical drinks.
Strawberries. Of all the non-citrus fruits, strawberries seem to be most required.
Pineapple. I chop up ripe pineapples and freeze them in Ziplocs for later use.
Coco Lopez. I’ve only ever found this in one specialty Mexican shop in Kensington Market in Toronto called Perolas Mexican Grocery on 247 Augusta. BYOB might stock this as well. I wouldn’t try using anything else in your Pina Coladas.
Dried Herbs. Herbie’s Herbs in Toronto is the Holy Grail of everything dried. They have EVERYTHING here and it is affordable. Take bags from the back of the pile for the freshest supply. They also sell Toronto’s cheapest vanilla beans.
Smuckers’ Red Raspberry Syrup. Unfortunately Smuckers’ true syrups aren’t available in Canada as far as I know. I had my Mom bring a couple bottles into Canada for me. She’s basically a Smuckers’ Smuggler.
Pomegranate Molasses. This magical stuff is found at specialty shops, Middle Eastern food stores and at Fiesta Farms in downtown Toronto.
Pure Vanilla Extract
Celery Salt, Tabasco & Worcestershire Sauce. These ingredients are obviously only important if you like making either the Bloody Mary or the better Bloody Caesar.
Orgeat. When I first started in cocktails, this almond syrup from Italy was hard to find. Lately I see it everywhere. In Toronto, you’ll find it at BYOB, Fiesta Farms and Festival Fine Foods. Luxardo makes a really nice version. Making this at home is a ton of work, apparently. I’ve never tried.
Q and Fever Tree Products. Both companies have upped the standard for basics like tonic and soda water. Fever Tree also makes a great Bitter Lemon Soda, which is otherwise really hard to find in Canada. Do not use carbonated mineral water as a substitute for soda water, as most do not contain sufficient carbonation.
Cola. There are still people who prefer a rum or rye and Coke. I think they’re just trying to be cool. For that reason it’s a good idea to keep a few cans on hand.
Ginger Beer. Many cocktails, especially in summer, call for this spicy Caribbean carbonated ginger soda. It can now be found in most grocery stores but if you’re having trouble, try a specialty grocer like Pusateri’s or Fiesta Farms. BYOB in Toronto stocks it as well. Ginger ale is not a substitute for ginger beer. Lots of people I know also make their own and many of the best bars only use homemade ginger beer.
Ginger Ale. I can’t think of very many cocktails that call for ginger ale other than maybe the Shirley Temples I make for my kids.
Carbonated Lemon Soda. When I first started making cocktails this British soda was hard to find. Of late, however, it has become more widely available. The San Pellegrino Limonata is a good option if you can’t find any of the British options. It is indispensible in a proper Pimm’s Cup.
Jujube Tea. Or any strange tea for that matter: Chinatown. End of story.