This will be a problem if there are long lines of sight - you will notice the ground sloping upwards even if it does so 10 km away. We can see ground sloping down and Earth's radius is over 6 Mm. The shorter the line of sight, smaller the radius can be without people noticing. Also, humans are used to ground sloping up due to hills, so I guess that as long as you restrict the line of sight to about 0.2r (so you see ground slope by at most 10 degrees), people will be (mostly) fine as far as sight goes. With somewhat claustrophobic design, this allows for a radius on the order of 100m. Also, in a station with a radius of approximately 200m and low ceiling, the floor would disappear behind the "horizon" of the ceiling close to the 40m line. Making the station 10 times larger would allow for view range of several hundred meters, which (judging by human depth perception limits) should be more than comfortable.
I guess humans lack the ability to feel a difference of less than 1 degree (or at least can ignore it). While standing still, the length of your feet would require a radius of about 15m. Walking would increase this to about 50m and spreading your arms would require about 100m radius. Running involves losing contact with the ground completely, so I expect the problem shifts to you needing to gain angular velocity as you accelerate. At full sprint humans reach up to 10m/s, meaning that if we wish to keep angular speeds below 1 degree/s we'd need a radius of about 600m.
If you wish to simulate Earth-like gravity, physics is your enemy. You'd want little variance between the gravity at floor and head level - the difference is proportional to change in radius, so a 1% variation would require about 200m radius. Also, precession forces are significant above 2 RPM, requiring over 200m radius to maintain 1g.
According to the wiki, NASA research led to the conclusion, that radii over 500m (implying about 1 RPM) are comfortable for people.
Humans adapt to almost anything non-lethal. Reducing gravity and forcing the brain to get used to some weirdness can easily push the required radius down. Visitors would hate it, but the locals would consider it natural. Other than that, a radius of 500m or more should be fine for most people.
Wikipedia pages on artificial gravity, space habitats and a few related concepts.
(Yes, I know, wiki is a bad source but this is not academia so give me a break.)