Health.
As anywhere else in tropical Africa there are many nasty things you can catch including malaria, but from a safety situation Ghana is relatively very safe. More about how to protect yourself on our Malaria Survival Guide.
Dangers.
Always take local advice and err on the side of caution when walking through remote areas, swimming (since aside from Bilharzia, there are strong tidal currents) and walking alone after dark in quiet, unlit places.
Women Traveling Alone.
As with all countries there are guys who will be looking to pick you up at beach areas, but as a woman alone you are pretty safe. Really more of an annoyance than a hassle, you may find that even with a male partner local men may take it on themselves to touch you - just don't take any shit and make sure you let them know this is not appropriate behavior and you or any other tourist is not going to stand for it.
When confronted most men are quite shy about having touched you. It's normally only brushing your arm rather than anything sinister, but it's not something they would do to a local girl (nor would they tolerate it).