While, at least in America, it's common for the bride to process to the altar where the groom awaits, the rubrics of the Roman Mass (and of the old Sarum rite) have the bride and groom processing to the altar together. I'm guessing that it's a Protestant innovation (that's become widespread even amongst Catholics), but when did the bride start coming forth to the groom rather than alongside him to the altar?
In Swedish tradition (which certainly is protestant), the bride and groom meet outside the church to proceed down the aisle together, to sginify that they are two free individuals that chose this voluntarily before God and the congration.
The tradition of the father handing the brude over to the groom is not universal.