Is there a way to make UITableView cells in iOS 7 not have a line break in the separator?

For iOS7:

if ([self.tableView respondsToSelector:@selector(setSeparatorInset:)]) {
    [self.tableView setSeparatorInset:UIEdgeInsetsZero];
}

For iOS8:

First configure your table view as follows:

if ([self.tableView respondsToSelector:@selector(layoutMargins)]) {
    self.tableView.layoutMargins = UIEdgeInsetsZero;
}

Then in your cellForRowAtIndexPath: method, configure the cell as follows:

if ([cell respondsToSelector:@selector(layoutMargins)]) {
    cell.layoutMargins = UIEdgeInsetsZero;
}

Note: Include both layoutMargins and separatorInset, to support both iOS versions