Yakuza series has drinking, Risen 2 has drinking minigame, Last Call you play a bartender

Redneck Rampage Collection
Just look at the screenshots.

Witcher.

Fallout games have various forms of alcohol. Personally, I don't like the long-term penalties like addiction. Other than the rare temporary boost to solve certain quests, I just collect them as loot to sell.

2064: Read Only Memories has a puzzle that involves giving characters drinks that match their taste.

VA-11 Hall-A is a game that revolves around being a bartender. I haven't played it myself though.

In Space Rangers HD: A World Apart, alcohol can traded for profit. However, alcohol may be illegal on certain planets, and
trading such items can cause a reputation loss.

In Jade Empire, the player can temporarily gain access to the Drunken Master style by consuming wine provided by a certain follower. While initially a powerful style, it loses its usefulness over time since the Drunken Style cannot be upgraded.

I think pretty much every Elder Scrolls will alter your stats when you drink alcohol (usually in a negative way, IIRC).

You can drink until you puke in the Fable-games. Same with Dead Rising.

You can drink alcohol in Bulletstorm, which will make your vision blurry, and you get more points for killing enemies while intoxicated.

S.T.A.L.K.E.R. series.

DUSK lets you drink beer and smoke cigars.
The former restores your Morale while the latter replenishes your Health.

There's Skooma in Morrowind and Oblivion. (Oblivion speedruns, for many categories, often duplicate a whole bunch of Skooma and use it for the speed boost (and the strength needed to carry all that Skooma); the run is then done entirely high on Skooma. Morrowind also offers some more tame beverages.

Ultima 7 also has a drug that boosts your stats temporarily, but once that wears of will lower your stats permanently.

In the Bard's Tale series, you can get a drink at a pub; a bard who drinks an alcoholic drink (Ginger Ale won't work) will recover all of their bard songs. (Don't know how the 2004 game and Bard's Tale 4 handle it, but I am pretty sure that BT4 bards are going to want alcohol.)

1) Fallout. Alcohol increases Charisma or Strength while lowering Intelligence. There's a chance of addiction, which makes the stat penalties stick until removed by a doctor or through other means.
The Witcher. I don't recall if it's different in the previous installments, but in The Witcher 3, you can heal by drinking alcohol. It makes your vision very blurry, which doesn't happen when healing by eating. So I found it pretty pointless and just collected booze to sell.
The Elder Scrolls. There's a deity named Sanguine, no doubt inspired by Dionysus/Bacchus. In Oblivion, you can make an offering of Cyrodilic Brandy at his shrine. In Skyrim, alcohol typically restores Stamina while temporarily lowering Stamina Regeneration. The effects were a bit more varied in previous installments.

2) Showing alcohol/cigarette/drug use is not the same as promoting it.
There's no such thing as second-hand drinking. It's possible to drink responsibly, but there's no reasonably safe amount of cancer sticks to consume. No alcohol addiction in Fallout and Fallout 2. In Fallout 3 Broken Steel and Fallout 4, you can take the Party Boy/Party Girl perk. In Fallout New Vegas, you can travel with Cass to get the Whiskey Rose perk.

Guild Wars 1 features several combat skills which provide an extra bonus when your character is drunk. For example:

Drunken Master: You move and attack 15% faster. If you are drunk, you move and attack 33% faster.
Dwarven Stability: Your stances last 100% longer. You cannot be knocked down if you activate this skill while drunk.
Feel No Pain: You gain +3 health regeneration. You also gain +300 maximum health if you are drunk when activating this skill. I've never been a smoker, but I do find it strange how strongly it's demonized now in certain media. While flipping through Netflix recently I noticed a movie said it was rated for Mature Audiences Only due to: extreme violence, blood and gore, allusions to rape and sexual violence, and... smoking. Those first three are acts which typically lead to life in prison or even the death sentence. And they're throwing smoking in with that lot?

IIRC in the Deus Ex games you can drink alcohol and smoke cigarettes. The first makes your vision blurry, the latter hurts you for one point (I think).
In Deadly Premonition you can smoke to make time go by faster.

The difference in depicting smoking contrary to drinking alcohol lies in the perception of (young) viewers. You see the hero having a smoke every five minutes and think: wow, what a cool guy. On the other hand, you see the same guy drinking one can of beer after the other and think: what a bum.
I guess, that´s the reason one gets banned, and the other not. IMO censoring or banning the depiction of such things in media is bullshit. Kids don´t start smoking or drinking because they see it in media, they do it because their friends or parents show them in real life.

Alone in the Dark. Edward Carnby could drink liquor. Eventually he could become drunk and affect actual gameplay.

Disco Elysium. Alcohol and drugs will raise stats, but come with a hefty penalty.

In Wing Commander 3 there is one situation where you can choose to get drunk and then fly the next mission under the influence.