逢う is often used for close friends, etc. and may be associated with drama or pathos; 遭う may have an undesirable nuance

to meet; to encounter; to see

Word usually written using kana alone; Esp. 遭う when in kanji

to have an accident; to have a bad experience

出遭う usu. has a negative connotation

to meet (by chance); to come across; to run across; to encounter; to happen upon

出会う／出合う only; Esp. 出合う

to meet (e.g. of rivers, highways, etc.)

出会う／出合う only; Often used imperatively as 出会え

to emerge and engage (an enemy)

meeting; rendezvous; encounter

meeting for the first time; coming across

Esp. 出合い, 出合

confluence

to meet fortuitously; to meet by chance; to happen across

rendezvous; tryst; (lover's) meeting; (secret) date

Dated term

clandestine meeting (of lovers); assignation; tryst; (lovers') rendezvous

to meet someone by chance; to happen upon

at last your time has come; I have found you at last

to face

till we meet again