There are the following pairs:

aller
 to go
venir
 to come
entrer
to come in
sortir
 to go out
arriver
 to arrive
partir
 to leave
moner
 to go up
descendre
 to go down
naître
 to be born
mourir
 to die

There are also the following verbs which don't fit into pairs:

passer to pass
rester to stay
tomber to fall
rentrer to go/come back home
retourner to go back
revenir to come back
devenir to become

With this method, you must remember that ALL reflexive verbs take être as well.