UICollectionView Horizontal Paging not centered

Remove spaces between items. For horizontal scrolling collection view set minimum line spacing to 0. You can do this with interface builder or with method of UICollectionViewDelegateFlowLayout protocol:

- (CGFloat)collectionView:(UICollectionView *)collectionView 
                   layout:(UICollectionViewLayout *)collectionViewLayout 
        minimumLineSpacingForSectionAtIndex:(NSInteger)section {
    return 0;    
}

Another way is making your cell's width less than collectionView's width for a value of horizontal space between items. Then add section insets with left and right insets that equal a half of horizontal space between items. For example, your minimum line spacing is 10:

- (CGFloat)collectionView:(UICollectionView *)collectionView
                   layout:(UICollectionViewLayout *)collectionViewLayout
        minimumLineSpacingForSectionAtIndex:(NSInteger)section {
    return 10;
}

- (CGSize)collectionView:(UICollectionView *)collectionView 
                  layout:(UICollectionViewLayout *)collectionViewLayout 
  sizeForItemAtIndexPath:(NSIndexPath *)indexPath {
    return CGSizeMake(collectionView.frame.size.width - 10, collectionView.frame.size.height);
}

- (UIEdgeInsets)collectionView:(UICollectionView *)collectionView 
                        layout:(UICollectionViewLayout *)collectionViewLayout 
        insetForSectionAtIndex:(NSInteger)section {
    return UIEdgeInsetsMake(0, 5, 0, 5);
}

And third way: manipulate collectionView scroll in scrollViewDidEndDecelerating: method:

- (void)scrollViewDidEndDecelerating:(UIScrollView *)scrollView {
    if (scrollView == self.collectionView) {
        CGPoint currentCellOffset = self.collectionView.contentOffset;
        currentCellOffset.x += self.collectionView.frame.size.width / 2;
        NSIndexPath *indexPath = [self.collectionView indexPathForItemAtPoint:currentCellOffset];
        [self.collectionView scrollToItemAtIndexPath:indexPath
                                    atScrollPosition:UICollectionViewScrollPositionCenteredHorizontally
                                            animated:YES];
    }
}

Swift version of @vlad-che accepted answer:

extension GoodsViewController: UICollectionViewDelegateFlowLayout {

    func collectionView(_ collectionView: UICollectionView, layout collectionViewLayout: UICollectionViewLayout, minimumLineSpacingForSectionAt section: Int) -> CGFloat {

        return 10
    }

    func collectionView(_ collectionView: UICollectionView, layout collectionViewLayout: UICollectionViewLayout, sizeForItemAt indexPath: IndexPath) -> CGSize {

        let frameSize = collectionView.frame.size
        return CGSize(width: frameSize.width - 10, height: frameSize.height)
    }

    func collectionView(_ collectionView: UICollectionView, layout collectionViewLayout: UICollectionViewLayout, insetForSectionAt section: Int) -> UIEdgeInsets {

        return UIEdgeInsets(top: 0, left: 5, bottom: 0, right: 5)
    }
}

Demo here in Swift 3: https://github.com/damienromito/CollectionViewCustom

func scrollViewWillEndDragging(_ scrollView: UIScrollView, withVelocity velocity: CGPoint, targetContentOffset: UnsafeMutablePointer<CGPoint>) {

    let pageWidth = Float(itemWidth + itemSpacing)
    let targetXContentOffset = Float(targetContentOffset.pointee.x)
    let contentWidth = Float(collectionView!.contentSize.width  )
    var newPage = Float(self.pageControl.currentPage)

    if velocity.x == 0 {
        newPage = floor( (targetXContentOffset - Float(pageWidth) / 2) / Float(pageWidth)) + 1.0
    } else {
        newPage = Float(velocity.x > 0 ? self.pageControl.currentPage + 1 : self.pageControl.currentPage - 1)
        if newPage < 0 {
            newPage = 0
        }
        if (newPage > contentWidth / pageWidth) {
            newPage = ceil(contentWidth / pageWidth) - 1.0
        }
    }
    self.pageControl.currentPage = Int(newPage)
    let point = CGPoint (x: CGFloat(newPage * pageWidth), y: targetContentOffset.pointee.y)
    targetContentOffset.pointee = point
}

Swift 4:

func scrollViewWillEndDragging(_ scrollView: UIScrollView, withVelocity velocity: CGPoint, targetContentOffset: UnsafeMutablePointer<CGPoint>) {

    let pageWidth = Float(itemWidth + itemSpacing)
    let targetXContentOffset = Float(targetContentOffset.pointee.x)
    let contentWidth = Float(collectionView!.contentSize.width  )
    var newPage = Float(self.pageControl.currentPage)

    if velocity.x == 0 {
        newPage = floor( (targetXContentOffset - Float(pageWidth) / 2) / Float(pageWidth)) + 1.0
    } else {
        newPage = Float(velocity.x > 0 ? self.pageControl.currentPage + 1 : self.pageControl.currentPage - 1)
        if newPage < 0 {
            newPage = 0
        }
        if (newPage > contentWidth / pageWidth) {
            newPage = ceil(contentWidth / pageWidth) - 1.0
        }
    }

    self.pageControl.currentPage = Int(newPage)
    let point = CGPoint (x: CGFloat(newPage * pageWidth), y: targetContentOffset.pointee.y)
    targetContentOffset.pointee = point
}