I would point out that in addition to the functional disadvantages (as expressed in the) responses below, you sould also consider if there are market disadvantages. Depending on the area and the style of home, the marketability of a home may be significantly effected, if it has no basement.
On he whole, we New Englanders like our basements. As you go further south or near a city (where people don't hang aroung long enough to accumulate a lot of stuff), basements are far less important.
Likewise, a basement tends to be a more important feature in a single family detached home than it is in a condo.
This is a question best addressed with your agent, as to what is acceptable, considering who a likely buyer of the home would be and what needs that buyer may have.
I'm wondering, what issue do you see? There's a lot of land that really isn't suitable for digging out basements.
Often, the furnace and water heater will be in a utility room at grade, and the water supply and ductwork will go over the ceiling, which isn't a terrible idea.
The problem is lack of space for the furnace, water pump and so on that would normally be in the cellar.
The other issue could be annoying and expensive. All of the water pipes are under the slab. If they leak or break you may have to rip the slab up to do a repair. There is no easy access like in a house with a foundation.
To add a basement you would have to have the house lifted, which would not only be very expensive but also tricky because the slab depends on the earth beneath it for support. Plus you would have to deal with the house resettling which could mean cracked walls, etc.
Could you add on to the home instead?