Based on its fixed-wing hypersonic design and inordinately high wing loading, I would predict that the X-15 has the highest recommend landing speed of any earthbound aircraft, with a preliminary search seemingly bearing this hypothesis out. According to an ostensibly legitimate NASA source (link below), the X-15's normal landing speed was 200+mph (173.8kts=321.9kph),
But if unofficial sources are to be believed, its actual landing speed was much higher, closer to 390kph=208kts (although these numbers are admittedly more dubious):
“According to an early edition of 'the Guinness book of world records' the X15 also holds the record for fastest landing speed at 242 mph compared with 210 mph for the space shuttle.”
If only powered aircraft are open to consideration, then the F-104 Starfighter would have to be up there as well. It needed a blown-flap flow control system just to be sane during landing...
“To make landing speeds “reasonable,” The F-104 forced engine air through the wings to smooth the airflow and give more lift. With bleed air, the Zipper could land at the challenging but not extreme speed of 160 to 165 knots. If the air-bleed system was not working, landing speeds climbed to 240 knots.”
So, if mechanical failure scenarios are deemed admissible, then the F-104 without its crucial boundary layer control systems would be the clear winner for powered landing speed, weighing in at an absolutely terrifying 240 kts. Otherwise, it would appear that the X-15 (unofficially) reigns supreme.