Good question! The truth is that there is no way to translate Homer to English, as Homeric Greek is an artificial language made up of multiple Greek dialects, of varying antiquity, all meshed together into a literary language whose feeling that cannot possibly be replicated in English or any other language.

Thus, what is a good translation will depend on what you want out of it!

Lattimore is probably the closest to Homer. He keeps the closest meter to the original, and the word choice too is very close to the Greek, but frankly I find some of his syntax and lines very stiff and gangly. Witness for yourself:

Sing, goddess, the anger of Peleus' son Achilles
and its devastation, which put pains thousand-fold upon the Achaians,
hurled in their multitudes to the house of Hades strong souls
of heroes, but gave their bodies to be the delicate feasting
of dogs, of all birds, and the will of Zeus was accomplished
since that time when first there stood in division of conflict
Atreus’ son the lord of men and brilliant Achilleus.

Fitzgerald is also considered up there, but quite simply I hate how many liberties he takes with the original Greek. You may judge for yourself:

Anger be now your song, immortal one,
Akhilleus' anger, doomed and ruinous,
that caused the Akhaians loss on bitter loss
and crowded brave souls into the undergloom,
leaving so many dead men—carrion
for dogs and birds; and the will of Zeus was done.
Begin it when the two men first contending
broke with one another— the Lord Marshal
Agamémnon, Atreus’ son, and Prince Akhilleus.

Most unforgivable at all, he often deletes epithets for the sake of poetry, which is an unsurpassable sin in my eyes for so much of Homer, and of oral poetry and story telling in general, is epithets, seeing how they characterize the characters and deities, and how they are played with. I can literally tell you, if you wish, how "swift-footed Achilles" connects with thousands-year-old lore of "swift" characters being connected with the wind and thus the wind-god Vayu who is a "brutish" warrior as comparable to the "chivalrous" warrior Indra, and that this tells you something about Achilles and Ajax the Lesser, the only "swift-footed" ones in the Iliad. Overall I don't like it, but you may judge for yourself.

Fagles is very similar:

Rage—Goddess, sing the rage of Peleus’ son Achilles,
murderous, doomed, that cost the Achaeans countless losses,
hurling down to the House of Death so many sturdy souls,
great fighters’ souls, but made their bodies carrion,
feasts for the dogs and birds,
and the will of Zeus was moving toward its end.
Begin, Muse, when the two first broke and clashed,
Agamemnon lord of men and brilliant Achilles.

I think Fagles is even less accurate to the Greek than Fitzgerald, but he sins less in the epithet territory. It's still really fucked though and the epithets are very awkwardly, "poetically" translated. I really like this one as poetry honestly, but not as Homer.

Emily Wilson is one of the more recent ones, it's also one of the few by a woman - Wilson keeps a nice iambic pentameter beat, while keeping things both accurate and nice-flowing:

Goddess, sing of the cataclysmic wrath
of great Achilles, son of Peleus,
which caused the Greeks immeasurable pain
and sent so many noble souls of heroes
to Hades, and made men the spoils of dogs,
a banquet for the birds, and so the plan
of Zeus unfolded—starting with the conflict
between great Agamemnon, lord of men,
and glorious Achilles.

She switches her lines around freely, she plays extremely loose with her precision. She adds "great" in line 2, and merges the first two Greek lines into three of her own. She also replaced Atreus' son with "Agamemnon" in the penultimate line (a recurring sin), also adding "great" which isn't in the Greek. She replaces the patronymics at random, uses the anachronistic “Greeks” (!!! What!!! I'd rather she used Aḫḫiyawan, if you get that Hittitological reference) throughout, and uses “glorious” instead of “godlike”. That said, her poetry is absolutely superb and keep the pace unlike anything else I've seen. I like how she translates the epithets differently depending on context, i.e. γλαυκός as "owl-eyed" or "grey-eyed" depending on how it's most appropriate at the moment. But I speak here as someone who has knowledge of the original Greek, of course. One of my favorites in any case - if you are looking for poetics, with decent accuracy, this is the one to pick, and the one I usually recommend to people.

Lombardo is actually the one I read with my partner:

RAGE:
            Sing, Goddess, Achilles’ rage,
Black and murderous, that cost the Greeks
Incalculable pain, pitched countless souls
Of heroes into Hades’ dark,
And left their bodies to rot as feasts
For dogs and birds, as Zeus’ will was done.
   Begin with the clash between Agamemnon—
The Greek warlord—and godlike Achilles.

He is not so literal to Homer, much like Fagles and Fitzgerald, but I find the usage of quick and short sentences in place of high and elevated ones to keep the sentiment of the Iliad as war poetry to be an absolute peak on that level. On the other hand, I dislike the use of anachronistic "Greeks" throughout instead of Danaans or Achaeans, as well as the lack of patronymics, etc. It's still recommended though, specially on audio.

I'm very impressed with Merrill's literalist translation:

Sing now, goddess, the wrath of Achilles the scion of Peleus,
ruinous rage which brought the Achaians uncounted afflictions;
many the powerful souls it sent to the dwelling of Hades,
those of the heroes, and spoil for the dogs it made of their bodies,
plunder for all of the birds, and the purpose of Zeus was accomplished—
sing from the time when first stood hostile, starting the conflict,
Atreus’ scion, the lord of the people, and noble Achilles.

Imo as accurate as Lattimore but with better poetry - I would recommend this one if you value accuracy over English poetics, it might be the best there.

Speaking of, I was greatly impressed Barry Nurcombe's translation, even though he's not even a classics professor but a fucking psychiatry professor. Still, it's a fantastic layman's translation:

1 Sing, Goddess, of the wrath of Pēleús' son
2 Akhilleús, the accursed wrath that caused
3 Akhaíans countless woes and hurled headlong
4 To Hādēs a host of heroes’ souls
5 And left their bodies spoil for dogs and all
6 The birds of carrion. The will of Zeús
7 Was brought to pass from when Agamémnōn,
8 The Lord of men, opposed the consummate
9 Akhilleús.

The issue is that the publisher put the verse numbers before the verses which is incredibly unpleasant and distracting! Whatever, I still recommend it.

You may window shop for Homer translations, what you'll like - and I doubt people would genuinely dislike the Iliad - depends on your taste, haha.

If you want to see things stretched to their limit, check out Alice Oswald's "Memorials" - it translates only the funereal laments of the Iliad, as well as the "biographical" verses of the dead verses, which Oswald correctly recognizes as belonging not to the epic genre but being the type of poems sung by bard-priests at funerals to appease the dead with their memory (you can see these types of ceremonies in Mycenaean larnax/sarcophagi paintings; I suspect that the Minoans used eunuchs to do it, for reasons that I could go on about for a hour). This turns the normal war poetry of the Iliad into an unrelenting funeral ceremony of nothing but young men being cried over by their mothers, wives, curses sent by loved ones to those who killed them, etc. It's quite riveting, I recommend it as a poem.

I hope this helped!