As a home owner, is there a risk to me if I hire an independent self-employed individual to do yard work and landscape maintenance around my home?

If they are injured due to your negligence, you could be liable for it. So, for example, say that there is a sinkhole on your property which you are aware of but have never filled in; if someone, say, breaks an ankle in it, you could be liable, since it would considered negligent to not remedy such a condition. Other possible sources of liability include if stairs, patio, deck, railings, etc. are defective or damaged and someone falls on them; if they use your ladders or tools, which are in poor repair or maintenance and cause injury; if  you're aware of dead/dying tree which injures or kills someone; if you have an animal which bites and do not restrain it; etc. On the other hand, if they are injured and you are not at fault in someway--e.g. a landscaper misuses his own mower--you should not face liability.

A good idea would be to have the individual sign a waiver disclaiming suing you for any injuries resulting from his work; such a waiver is not absolute and will not protect you if you were grossly negligent (more than orginarily careless), but will provide some protection. Also, you should make sure the person has and provides evidence of insurance--because you also want to be able to recover from him is he causes any injuries or property damage to you.