I'll be needing to do exactly the same thing - get all the tiles that are overlapping a sprite. There doesn't appear to be a built-in function, and I agree this seems like something that would be very useful for many, many people. I'd also like to be able to query tile size for different tilemaps at runtime, but that's another thread.
Anyway, since we don't seem to have what you're looking for I have some suggestions you can try, with the caveat that I haven't tried them myself yet.
You can test points along the edges of your character sprite (not just the default image point) using Tilemap.PositionToTileX() and Tilemap.PositionToTileY(). Assuming your default image point is in the center of your character sprite, this will give you the X position of the right edge of the sprite:
Tilemap.PositionToTileX(Player.X + Player.Width/2)[/code:3nwja19w]
And this will give you the Y position of the [i]bottom edge[/i] of your sprite:
[code:3nwja19w]Tilemap.PositionToTileY(Player.Y + Player.Height/2)[/code:3nwja19w]
Together that gets you the bottom-right corner of the sprite. Do that for all the corners and perhaps for the midpoints of all the sides and you have a pretty good idea whether your character is overlapping specific tiles.
You could also manually define some image points around the edges of your sprite. I.e., add an image point the the bottom-right corner of your sprite and name it "BottomRight", then query it like this:
Not exactly perfect solutions but better than nothing; if I come across something bulletproof I'll post it. Good luck!