be familiar with 一般是指某人熟悉某人、某物：
例句：
I'm not familiar with this computer.我不熟悉这台电脑.
Oh,at the end some songs that everyone's familiar with,then they can join in.噢,在晚会快要结束时来几首大家都熟悉的歌曲,那样听众就可以跟着唱.
be familiar to 则是某物、某事为某人所熟悉：
例句：
The name seems familiar to me 相当于I seem familiar with the name.这个名字我似乎是很熟悉的.