To cross over a place or space to the opposite side
When to use
Crossing a road, Crossing a river, Crossing a street distance
The nuance
Indicates the act of crossing without emphasizing direction toward the speaker's side.
건너다 (geon-neo-da, geonneoda) · 건너오다 (geon-neo-o-da, geonneooda)
건너다 means simply crossing a place, while 건너오다 emphasizes crossing towards the speaker's side or location.

One lane per word — no nested boxes, just the gist.
To cross over a place or space to the opposite side
When to use
Crossing a road, Crossing a river, Crossing a street distance
The nuance
Indicates the act of crossing without emphasizing direction toward the speaker's side.
To cross over toward the side where the speaker or listener is
When to use
Crossing toward home, Crossing toward the classroom, Crossing toward the store
The nuance
Emphasizes crossing toward the speaker's or listener's location.
길을 건너다.
gil-eul geon-neo-da., gil eul geon neo da.
Simply crossing the road; 건너다 is appropriate.
길을 건너오다.
gil-eul geon-neo-o-da., gil eul geon neo o da.
Crossing the road toward the speaker; 건너오다 is correct.
강을 건너오다.
gang-eul geon-neo-o-da., gang eul geon neo o da.
Crossing the river toward the speaker's side; 건너오다 fits.
강을 건너다.
gang-eul geon-neo-da., gang eul geon neo da.
Simply crossing the river; 건너다 is correct.
나는 집에서 학교로 건너오다.
na-neun jip-e-seo hak-gyo-ro geon-neo-o-da., na neun jip e seo hak gyo ro geon neo o da.
Speaker starts at home going to school; 건너가다 should be used, not 건너오다.
그는 길을 건너다 왔어요.
geu-neun gil-eul geon-neo-da wass-eo-yo., geu neun gil eul geon neo da wass eo yo.
He crossed the road and came here; 건너다 와도 자연스럽다.
그는 길을 건너오다 갔어요.
geu-neun gil-eul geon-neo-o-da gass-eo-yo., geu neun gil eul geon neo o da gass eo yo.
건너오다 means coming toward speaker, so combined with 갔어요 (went) is incorrect.
아이들이 거리 건너다 놀고 있다.
a-i-deul-i geo-ri geon-neo-da nol-go iss-da., a i deul i geo ri geon neo da nol go iss da.
Children crossing the street; 건너다 is appropriate.
Which word is appropriate to express crossing toward the speaker?
What is the correct expression for simply crossing a river?
Which sentence is incorrect? 'He crossed the road and went.'