Laudator Temporis Acti

John 11.35: "Jesus wept." Some in the ancient world might have interpreted the act of weeping as evidence that Jesus was not God. See Anthony Corbeill, "Weeping Statues, Weeping Gods and Prodigies from Republican to Early-Christian Rome", in Thorsten Fögen, ed., Tears in the Graeco-Roman World (Berlin: Walter De Gruyter, 2009), pp. 297-310 (305-307 = "Real Gods Don't Cry"), to which I'm indebted for knowledge of some of the passages quoted below.

Euripides, Hippolytus 1396, first states the rule (Artemis speaking, my translation):

It is not lawful for me to let fall a tear from my eyes.

κατ' ὄσσων δ' οὐ θέμις βαλεῖν δάκρυ.

Ovid restates the rule at Metamorphoses 2.621-622 (tr. Frank Justus Miller):

For the cheeks of the heavenly gods may not be wet with tears.

                      neque enim caelestia tingui
ora licet lacrimis.

and Fasti 4.521 (tr. James George Frazer):

For gods can never weep.

neque enim lacrimare deorum est.

Cf. also Friedrich Marx's emendation of Ovid, Metamorphoses 14.420:

nec satis est nymphae flere et lacerare capillos       420
et dare plangorem: facit haec tamen omnia, seque
proripit ac Latios errat vesana per agros.

420 satis codd.: fas F. Marx, Rheinisches Museum für Philologie 41 (1886) 559

The contrary to fact condition in Naevius' epitaph (Aulus Gellius, Attic Nights 1.24.2, tr. J.C. Rolfe) also implies the existence of this rule:

If that immortals might for mortals weep,
Then would divine Camenae weep for Naevius.

inmortales mortales si foret fas flere,
flerent divae Camenae Naevium poetam.

Despite the rule, classical literature provides several examples of gods (or, more often, goddesses) weeping. A selection follows.

Homer, Iliad 21.493-426 (tr. A.T. Murray):

Then weeping the goddess fled from before her even as a dove that from before a falcon flieth into a hollow rock, a cleft—nor is it her lot to be taken; even so fled Artemis weeping, and left her bow and arrows where they lay.

δακρυόεσσα δ᾽ ὕπαιθα θεὰ φύγεν ὥς τε πέλεια,
ἥ ῥά θ᾽ ὑπ᾽ ἴρηκος κοίλην εἰσέπτατο πέτρην
χηραμόν· οὐδ᾽ ἄρα τῇ γε ἁλώμεναι αἴσιμον ἦεν·
ὣς ἣ δακρυόεσσα φύγεν, λίπε δ᾽ αὐτόθι τόξα.

Callimachus, Hymns 6.17 (hymn to Demeter, tr. Neil Hopkinson):

No, no! let us not speak of what brought tears to Deo.

μὴ μὴ ταῦτα λέγωμες ἃ δάκρυον ἄγαγε Δηοῖ.

Philicus of Corcyra, Hymn to Demeter (Supplementum Hellenisticum, fragment 680), line 40 (possibly referring to the creation of a spring from Demeter's tears, my translation):

You will bring forth a spring with your tears.

σοῖς προσανήσεις δακρύοισι πηγήν.

Nonnus, Dionysiaca 6.8-9 (on Deo = Demeter, tr. W.H.D. Rouse):

The cheeks of the goddess were moistened with self-running tears.

                                     βαρυνομένης δὲ θεαίνης
δάκρυσιν αὐτοχύτοισι καθικμαίνοντο παρειαί.

Vergil, Aeneid 1.227-229 (tr. H. Rushton Fairclough):

And lo! as on such cares he pondered in heart, Venus, saddened and her bright eyes brimming with tears, spake to him...

atque illum talis iactantem pectore curas
tristior et lacrimis oculos suffusa nitentis
adloquitur Venus...

Vergil, Aeneid 10.628 (tr. H. Rushton Fairclough):

And Juno weeping...

et Iuno adlacrimans...

Ovid, Amores 3.9.45-46 (on Venus, tr. Grant Showerman):

She turned her face away who holds the heights of Eryx; some, too, there are who say she kept not back the tear.

avertit vultus, Erycis quae possidet arces;
  sunt quoque, qui lacrimas continuisse negant.

Propertius 2.16.54 (on Jupiter, tr. G.P. Goold):

Since he too, although a god, has been deceived and wept.

deceptus quoniam flevit et ipse deus.

Propertius 4.11.60 (on Augustus, tr. G.P. Goold):

And we saw a god's tears flow.

et lacrimas vidimus ire deo.

Claudian, Rape of Proserpine 1.192-193 (on Ceres = Demeter, tr. Maurice Platnauer):

Ah, how often, foreknowing of coming ill, did she mar her cheek with welling tears!

heu quotiens praesaga mali violavit oborto
rore genas!

Related post: Did Christ Ever Laugh?