Allow setting minimum size of the rows and columns:
I don't know at design time how many items there will be in the tileview, so if I set fixed height and width for items I can have the control using only 1/10 of the available space, but if I don't set them I can have many too-small items which content cannot be properly displayed.
I need a minsize for the items so if I have few items they have a variable size and if they are a lot they use the scrollbars.

Add support for IsSynchronizedWithCurrentItem

Add SingleNoToggle selection mode. In this mode the TileViewItem won't unselect on click.

Design time error occurs when setting MinimizedRowHeight

Implement command support for events like TileStateChanged. Allow sending the TileItem, which state is changing, as an argument.

Add a build-in paging support for the RadTileView.

Add GridSplitters between the columns and rows of the TileView so that rows and columns can be resized.

GridSplitters should be available when the tiles are restored or Minimized/Maximized. In the latter case, only a vertical one should be available to resize the minimized tiles' width in respect to the maximized one.

Implement a touch swipe scrolling for RadTileView

Allow more than one maximized tile

Both events must be raised only once per item. Also, the event arguments of each event must contain a reference to the item that begins/ends its layout change.

TileView: Allow users to see the TileViewItem OldState property

TileView: Add ToggleButtonStyle

Add animations for items collection change (add/remove)

Add TileViewItem.HeaderBackground property.

DECLINED: There is SDK sample available demonstrating how you can change the background color of the header of each item.
https://github.com/telerik/xaml-sdk/tree/master/TileView/ChangeHeadersBackground

Visualize drop zone (dashed line in iGoogle)

Allow users to specify custom panel for the MinimizedItems. The specific request is the minimized items to be rendered in two columns.

In application with heavier styles and a slower machine when items are dragged and swiped it sometimes leads to exception:
Cannot animate the 'VerticalOffset' property on a 'Telerik.Windows.Controls.TileViewPanel' using a 'System.Windows.Media.Animation.DoubleAnimationUsingKeyFrames'

Implement a mouse wheel support for the Horizontal ScrollBars of the control

The Header of the TileViewItems is bound only for the first X tiles, where X is the loadsize of the VirtualQueryableCollectionView

ScrollViewer property needed like in RadTreeview