here are some lines i gathered while reading the iliad. Some are of proverbial character while others express the anthropology in homer - the way the epics view men, their relations to gods etc. i find all of them to be beautiful poetry. Feel free to add more!
1.41-42 Chryses to Apollon
… to de moi krêênon eeldôr:
tiseian Danaoi ema dakrua soisi belessin.
1.45 about Apollon’s descent
…ho d’ êïe nukti eoikôs.
the god of light descending like night? or is the connection of apollon and light a later one?
2.356
tisasthai d’ Helenês hormêmata te stonachas te.
The well known multi-genitive.
3.57 Hektor to Paris
alla mala Trôes deidêmones: ê te ken êdê
laïnon hesso chitôna kakôn henech’ hossa eorgas.
3.221
all’ hote dê opa te megalên ek stêtheos heiê
kai epea niphadessin eoikota cheimeriêisin,
ouk an epeit’ Odusêï g’ erisseie brotos allos:
ou tote g’ hôd’ Odusêos agassameth’ eidos idontes.
this - the “epea niphadessin eoikota cheimeriêisin” image - strikes me as profoundly modern. Proves again that great poetry is in way timeless. This could be a line by Rilke or Breton.
3.350-54
Atreïdês Menelaos epeuxamenos Dii patri:
Zeu ana dos tisasthai ho me proteros kak’ eorge
dion Alexandron, kai emêis hupo chersi damasson,
ophra tis errigêisi kai opsigonôn anthrôpôn
xeinodokon kaka rhexai, ho ken philotêta paraschêi.
4.43 Zeus to Hera
kai gar egô soi dôka hekôn aekonti ge thumôi
weird. A prototypical disjuction between phronesis and thumos (hekon- aekonti)
4.442-444 on Eris
hê t’ oligê men prôta korussetai, autar epeita
ouranôi estêrixe karê kai epi chthoni bainei:
4.450-456
entha d’ ham’ oimôgê te kai euchôlê pelen andrôn
olluntôn te kai ollumenôn, rhee d’ haimati gaia.
hôs d’ hote cheimarroi potamoi kat’ oresphi rheontes
es misgankeian sumballeton obrimon hudôr
krounôn ek megalôn koilês entosthe charadrês,
tôn de te têlose doupon en ouresin eklue poimên:
hôs tôn misgomenôn geneto iachê te ponos te.
5.440-442 Apollon to Diomedes
…mêde theoisin
is’ ethele phroneein, epei ou pote phulon homoion
athanatôn te theôn chamai erchomenôn t’ anthrôpôn.
6.146-151 Glaukos to Diomedes
hoiê per phullôn geneê toiê de kai andrôn.
phulla ta men t’ anemos chamadis cheei, alla de th’ hulê
têlethoôsa phuei, earos d’ epigignetai hôrê:
hôs andrôn geneê hê men phuei hê d’ apolêgei.
This is one of my favorite lines in the entire epics. truth hurts as they say.
6.208
aien aristeuein kai hupeirochon emmenai allôn
the well known maxim; greek men nowdays take the pleasure of seeing this in the military camp entrances as they come in for their obligatory military service. bliah.
6.168
sêmata lugra
6.357
hôs kai opissô
anthrôpoisi pelômeth’ aoidimoi essomenoisi.
these self-referencial lines - in a way it feels as if the poet speaks himself - that express a wish which came true (since these mortal heroes are got their immortal song) always makes me feel sad and nostalgic..
Especially that one from Odyssey:
Od.3.113
tis ken ekeina
panta muthêsaito katathneton anthrôpôn
which Joyce takes up in Ulysses inverted as: who watches me here? who will ever anywhere read these written signs?
6.202
hon thumon katedôn, paton anthrôpôn aleeinôn
6.484 Andromache
dakruoen gelasasa
7.90 Hektor
to d’ emon kleos ou pot’ oleitai.
8.558
ouranothen d’ ar’ huperragê aspetos aithêr
great image.
(i’ve lost everything from book 9 to book 16 
)
i only remember this one:
11.368
ton d’ ou tarbêsas prosephê krateros Diomêdês:
toxota lôbêtêr kerai aglae parthenopipa
funniest ever:)
17.446
ou men gar ti pou estin oïzurôteron andros
pantôn, hossa te gaian epi pneiei te kai herpei.
17.647 Aias praying
en de phaei kai olesson
!!!
18.309
xunos Enualios, kai te ktaneonta katekta.
perhaps an anticipation of Polemos pater panton?
20.131
chalepoi de theoi phainesthai enargeis
22.199 hunting Hektor
hôs d’ en oneirôi ou dunatai pheugonta diôkein.
23 and 24 also lost:(