I formed an LLC in one state to provide software consulting services from my home in another state, do I need to register as a foreign LLC with my home state?

You will need to register as a foreign LLC in every state that you do business in.  Each state defines "doing business" differently.  However if you or an agent of your LLC physically perform any sort of business in the state or you have income from that state then it is likely that you are "doing business" in that state.  Maintaining bank accounts, selling through independent contractors, holding shareholder meetings, or responding to lawsuits are example of activity that is not consider as "doing business".  I have given you just some rough guidelines.  Meet with a business attorney in your state for a more accurate answer.