Dark & Stormy or a Moscow Mule are both nice, but my go-to is a Caucasian.
I rather have some kind of rum and cola, or regular margarita if I’m not having having straight vodka, but the vodka martini, shaken not stirred is the coolest drink to order, so I do it anyway.
G&T for me, as well. I’m not a big fan of gin. I’m not a bit fan of tonic. Yet together, with a bit of lime, it transcends the sum of its parts.
But I also like a good bloody mary, and a margarita on the rocks, easy-to-no simple syrup.
I’m not a big cocktail drinker, but those are my go-tos. Even a nice gin gimlet up every once in awhile.
Rye old fashioned, or a Manhattan made with Copper Fox rye.
I love a gin and tonic made with Fever Tree tonic, with a wedge of lime. Weirdly I’m the opposite of Joey P - I like tonic on its own too, like Tanqueray, and hate Beefeater.
I made an epic mint julep last week. Talk about a drink that’ll put you under the table. I use mint from the plant on my front porch, and it’s divine and all too easy to slurp down.
I also love a White Lady. I actually had a bartender come out to my table and congratulate me on my drink order when I asked for one at a restaurant!
My husband and I have a cocktail hour every evening. Our favorite standby is gin & tonic, made with Tanqueray Rangpur or (sometimes for me) Bombay Sapphire.
In the summertime sometimes we’ll get on a mojito or caipirinha kick. We use Bacardi white rum for both–cachaca is too expensive.
My very favorite drink, though it’s a pain in the ass to make, is the New Orleans gin fizz.
An extra spicy Bloody Mary. When another bartender walked past the guy making me a Bloody Mary and saw all the Tabasco he was putting in, the bartender grabbed the guy’s hand and asked him what the hell he was doing. Making me happy, that’s what.
not much of a drinker anymore - but I liked the following if vague memory, police records, transcripts of divorce proceedings and interesting physical, mental and emotional scars seem to indicate
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Blue Monday - Creme De Cacao, Vodka and 7 up.
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Silver Fizz ( for when I was in a Fitzgeraldian sort of mood)
-a complex drink involving gin, soda water, lemon rind and egg white, which must be mixed and served with precision in exactly the right glass. I could be a nasty drunk… -
The Blue Jock - a Cocktail of my own invention -2/3 Blue Gatorade and 1/3 Vodka, tasty and the electrolytes helped keep the hang overs at bay.
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Rum (dark) and Cola, although I liked it with flat cola at room temp.
That’s about it for mixed drinks, really, usually it was “I’ll have what your having…” and then i would wake up three days later with my pants on backwards…
Just a note to add, that I don’t miss those days or the drinks, and wish all of you well in your pursuit of the perfect cocktail/mixed drink.
Cheers! (Toasts with a Mug of green Tea)
A dirty gin martini of sorts for me. Low ball glass with ice cubes, teaspoon of green olive juice, 1/2 teaspoon vermouth, 2oz Beefeaters London dry gin and a splash of water. Stir with 3 green olives on a toothpick. It works for me.
Bloody Marys sometimes.
I had my first Dark & Stormies at a boat club and they did things a little differently, using spiced rum and a splash of bitters with the lime juice and hot ginger beer. This is what I tend to drink when its hot outside. I also like a simple G&T: shot of Gin over ice, splash of lime, top with Tonic. As others have noted, the Brits came up with a solution to making quinine palatable - just add booze.
-DF
In the non-alcoholic realm I absolutely love Coca Cola mixed with coffee
When it comes to drinking, I’m a traditionalist. Pretty much the only mixed drinks I do are:
Gin & Tonic (usually specifiy Tanqueray, but with the tonic it doesn’t matter that much)
Rum & Coke
A classy Bloody Mary - I’m not talking V8+vodka, I know a couple of restaurants that make them more like a refreshing glass of spicy liquid vegetables with some vodka to get the morning started right.
…and also, it’s crass as hell, but when I’m in Vegas and mean to be gambling late, Red Bull+Vodka. Tastes terrible, but works. 
My go to straight drinks are whisky, neat, or a martini: Sapphire, up, olives - not stuffed. A dirty martini now and then is nice too.
Actually, I had this for the first time a year or two ago at a restaurant that one of my co-workers owned. Delicious. My first appreciation of dark rum; sometime I’ll sip it straight, but with ginger and lime it is tasty.
Not really a “mixed drink” but my favorite is Canadian Club, rocks, splash of water.
A nice simple vodka tonic with lime is lovely.
As for drinks I wouldn’t make myself, a mojito is never a bad idea.
Ever since I started experimenting with espresso, back in my high school grocery-store-clerk days, I’ve really enjoyed espresso with a Coca-Cola chaser.
As to cocktails: Well, truth is, I’m not much of a cocktail drinker; mostly I stick to beer. But if you want to know my favorite (and arguably, it’s not even a cocktail; as Peggy Olson pointed out, you need three ingredients for it to be a cocktail), it’s a caipirinha. Made with a cheaper cachaça, because that’s how they do it in Brazil (also, Leblon tastes like paint stripper). If you’re lucky and find a place that’ll do it with a slice of sugar cane as a garnish–heaven.
I’m also fond of a classic 3-2-1 margarita (3 parts tequila, one part triple sec or whatever similar thing–I used Patron Citronge, and 1 part lime juice). Spent a few weeks watching I, CLAVDIVS every Friday night with a few of those back in law school. Certain to give you heartburn, and also certain, because five of those six parts are 80 proof liquor, to get you nice and toasty. Did manhattans for a while; don’t know if I could now. Scotch and soda is another go-to when I’m at an open bar. Finally, as many have noted, a G&T done well is divine. For some reason, I can’t mix one properly at home, though.
I’m astonished at the number of G&T drinkers! I’m in good company. 
For me, it’s a couple ounces of Tanqueray, not Bombay, cuz I like the bite, lots of fresh lime and topped off with how much Schweppes it takes to fill the glass.
Heaven…
My wife and I have consumed more than our share of caipirinhas and mojitos over the years.
We also like French 75s- the brandy variant, not the gin one, which is basically a Tom Collins with champagne instead of the soda.
Other than those, we do break out the cocktail books and try different stuff pretty often- Ramos Gin Fizzes are awesome, but like you said, a pain to actually crank out.
We also have the occasional Sidecars, Cable Cars, Margaritas and Palomas as well.
Summer: Gin and Tonic.
Bombay Sapphire is the preferred Gin. Schweppes is the preferred Tonic, although whilst in Paris Mrs_Doom (also a G&T drinker) and I were served Schweppes Indian Tonic, of which we’d never heard, nor seen around here, and it was delicious.
Winter: Hot Toddy.
Spiced Rum, sugar, boiling water. Rum and sugar to taste. Sometimes I will also add a splash of Bailey’s, or even table cream, depending on mood.
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Sugar
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Lime
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Cachaca
For a couple of years I tried t omake a clasic margarita that tasted good, but all we could taste was the pucker of the lime juice. Finally I broke down and started adding just a bit of simple syrup to the mix, and it went from something to endure to something joyous. No purist here, but I do love me some homemade margaritas while sitting on the porch at the beach.