Most domestic UV light sources are of low power and intensity and are unlikely to cause significant harm on a short-term basis.
There has been some concern of UV LEDs because of their narrow beam and essentially point source nature allowing extremely precise focussing - potentially allowing a very high concentration of light to impact the cornea or retina. Most UV LEDs are very low power - typically less than 5 mW of UV radiation output.
Higher power sources could potentially be more dangerous, but these are not readily available in LED form. Industrial UV sources are often high-power discharge type lamps (expensive, bulky and fragile), and these can produce extremely intense well focussed energy.
One interesting problem is new high-power LEDs. I have some blue LEDs which are 'Class 2' rated for eye safety (essentially this means that there is the potential for eye damage if you look directly at them - although if you read the safety literature carefully, there is no evidence to suggest that they are directly harmful, it is only concern over the very high output of short wavelength radiation). To put it in perspective my LEDs have a blue radiation output of about 400 mW (this compares to about 6 mW, for one of ebay's best blue LEDs). Although unlikely to cause injury, these are high energy devices, and are a near point-source, so potentially the eye could focus the light to a very small point, which could cause retinal damage.
To put it in perspective, I've use a 1000 mW laser and it will certainly set bits of paper on fire - and can burn through retinas in a few seconds.
