What are good alcohol-free fragrances for Muslim men?

Yes, there are plenty of good alcohol-free choices. Look for attar (perfume oil), roll-on or solid perfumes, bakhoor and oud, or sprays clearly labelled alcohol-free. To be sure, read the ingredient list: the words to watch for are alcohol denat., SD alcohol, ethanol and isopropyl alcohol.

Why choose alcohol-free?

Most contemporary scholars allow perfume that contains alcohol, since it's worn and not drunk. Some Muslims still prefer to avoid it to stay clear of doubt, especially before prayer, and alcohol-free scents let you do that without giving up on smelling good. See Is perfume with alcohol haram?

Smelling pleasant is a sunnah. The Prophet ﷺ never turned down a gift of perfume (Sahih al-Bukhari 2582), so a good scent is something to enjoy, not to feel guilty about.

Types to try

Attar (ittar): a concentrated oil, usually from flowers, wood or resin, in a tiny bottle. A dab lasts for hours. See What is attar and why do Muslim men wear it?
Perfume oils and roll-ons: the same idea in a carrier oil like jojoba or fractionated coconut oil. Easy to carry and not overpowering.
Solid perfumes and balms: wax-based, with no liquid alcohol, and good for travel.
Bakhoor and oud chips: burned as incense for your home, clothes or beard. Ibn Umar burned aloeswood, sometimes with camphor, and said this was how the Prophet ﷺ did it (Sahih Muslim 2254).
Alcohol-free sprays: a growing number of brands make them, often water- or oil-based.

Scent families men often like

Oud (agarwood), sandalwood, amber, musk, cedar, saffron, rose and vetiver are common choices. Woody and resin scents suit many people, while lighter citrus or green notes are good for summer and work. Test any scent on your skin first, because it smells different on everyone.

How to read the label

Watch for: alcohol denat., SD alcohol 40-B, ethanol, isopropyl alcohol.
Usually fine: cetyl, cetearyl and stearyl alcohol. These are waxy "fatty alcohols" used in lotions and creams, and they have nothing to do with drinking alcohol.
"Perfume oil" or "attar" on the front: still check the back. Some sprays sold under these names contain alcohol.
"Parfum" or "fragrance": doesn't list what's inside. If a brand won't tell you, choose another.

Wearing it well

Dab a small amount on your wrists, neck or beard, not on a white thobe, since oils can stain.
Go light for the mosque, where people stand shoulder to shoulder. Strong oud can give others a headache.
Keep your clothes and body clean first. Perfume is a finishing touch, not a replacement for a shower.

Not sure what suits you? Some men's scents are marketed as unisex or as women's. See Can Muslim men wear women's or unisex fragrances?

Key points

Attar, perfume oils, solid perfumes and bakhoor are naturally alcohol-free.
Check labels for alcohol denat., SD alcohol, ethanol and isopropyl alcohol.
Fatty alcohols like cetyl alcohol are not drinking alcohol.
Wear scent lightly, especially to the mosque.

Tip: Buy a small 3 ml bottle of attar before a big one. If the scent still smells good on your skin after a few hours, it's worth keeping.