When getting funding from family and friends, are term sheets necessary? The family member I've approached is more interested in becoming an investor, rather than owning convertible debt. Every term sheet I've come across has been for a round of financing, but are there any examples for just one investor?
Yes, I highly recommend putting the details of a family member's investment in writing.
Some people think that wanting to put something in writing indicates a lack of trust between the parties, but that is not the only reason. In discussing an investment orally, many details may not be thought out or be left unsaid. For some important details, you could have a different understanding than the investor but not realize it. By writing it down, you make the terms of the investment clear for everyone's benefit.
Since there is presumably not a trust issue between you and your familial investor, you could leave out some of the boiler plate and legalese to make it more friendly, but the terms of the investment should be as complete as possible.
Note that you want a final agreement and not a term sheet (http://en.wikipedia.org/wiki/Term_sheet). A term sheet is a preliminary agreement, which can be useful in complicated business situation but which you probably do not need here.
I don't have any agreement I can point you to, but including "angel" or "seed" in your Google search should get you what you need.
Definitely put all agreements with anyone in writing and have these reviewed by your attorney and strongly recommend that any and all of your investors engage their own counsel to review the agreements.
These agreements need to cover a broad range of circumstances and topics - corporate governance, what happens if someone offers to buy some of your stock, how profits flow, etc.
Good agreements protect both you and your investors and in the case of family members, help ensure that you'll be able to eat Thanksgiving dinner together many years in the future.