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This ingredient gets a bad rep because it is irritating and drying due to its astringent property. Astringents draw out natural oils in tissue to constrict pores and dry out your skin.

However, alcohol denat. is not all that bad.

Due to its low molecular weight, alcohol denat. tends to evaporate quickly. One study on pig skin found half of applied alcohol evaporated in 10 seconds and less than 3% stayed on skin.

This also helps other ingredients become better absorbed upon application.

Studies are conflicted about whether this ingredient causes skin dehydration. One study from 2005 found adding emollients to propanol-based sanitizer decreased skin dryness and irritation. Another study found irritation only occurs if your skin is already damaged.

Small amounts of alcohol are generally tolerated by oily skin or people who live in humid environments.

The rule of thumb is this ingredient will probably not affect your skin much if it is near the end of an ingredients list.

One thing to note:
People with ALDH2 (aldehyde dehydrogenase 2) deficiency may experience skin irritation from continued alcohol use. About 8% of the world's population have this deficiency.

The Cosmetic Ingredient Review Expert Panel has determined denatured alcohols to be safe for use in concentrations between 0.05% and 12% (depending on which denaturant is used).

Also...

This ingredient has antimicrobial and solvent properties.

The antimicrobial property helps preserve products and increase their shelf life. As a solvent, it helps dissolve other ingredients.

Look for formulas that contain glycerin, hyaluronic acid, or panthenol if you want to offset any drying effect.

This ingredient will trip away your skin's natural oils/lipids that help it lock in moisture. This can worsen dryness, trigger eczema flare-ups, and aggravate rosacea.

Be sure to patch test any product with this ingredient if you have dry or sensitive skin, eczema, or rosacea.

There's some lab work behind its reputation; in one study, it acted as an antioxidant and calmed inflammation in human immune cells. But it also killed skin cells (keratinocytes) in a dish.

It stopped damaging those cells and still reduced swelling in mice when the researchers wrapped it in tiny capsules to slow its release.

One study that is quoted out of context frequently: clove oil killed human skin and blood vessel cells at levels as low as 0.03%, and about 73% of that came down to eugenol. Keep in mind those were bare cells sitting in a dish with no skin barrier in the way (which is a lot harsher than what happens on your actual face).

On concentrations, it is restricted to 0.64% in leave-on products + body products, 0.21% in baby + lip products, 2.5% in fine fragrance and 4.9% in rinse-off. Real formulas usually land far below those caps.

Allergy is the actual story with this ingredient. It is one of the eight markers dermatologists use for allergy testing, and the EU requires it to be named on the label above 0.001% in leave-on and 0.01% in rinse-off products.

It is also a prohapten, meaning it needs enzymatic activation in skin to become allergenic, so sensitivity varies between people.

Rates are modest but not trivial: in a classic EECDRG multicentre study, 13 of about 1,300 patch-tested patients reacted to eugenol, and in eugenol-allergic subjects the lowest positive patch test concentration was 0.031%, with 56% reacting in a 21-day repeated open application test at 0.5% to 2.7%.

Normal use levels are generally fine if you are not already sensitized.