I have an old Minolta Maxxum, is there a camera DSLR body that will take all the lenses from the Maxxum available ?
Yes, there are. Any digital camera with an A-mount will accept them directly. The Sony A68 is the latest such model and uses an APS-C sensor so it will crop the field of view by 1.5X, meaning all your lenses will become less wide but they will still work. To preserve the field-of-view, you can use a full-frame model such as the Sony SLT-A99V.
There is another good option and that is to with a Sony E-mount mirrorless camera and an additional adapter. These some in two varieties and coverage-size, one with Phase-Detect AF which will allow the camera to also perform autofocus with your Maxxum lenses. Some newer models can do it without the Phase-Detect adapter because they have built-in Phase-Detect AF.
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1May want to add "A-mount" or "dSLT" to Alpha in your first sentence, given that both A-mount (alpha) and E-mount (NEX) cameras now both come under the Alpha label. – inkista Nov 16 '15 at 22:32
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Note that when using the adapter with built-in Phase-Detect AF and non-AF lenses the lenses must first be brought fairly close to the correct focus setting manually. The adapter can't, for example, bring a lens physically set at infinity to focus near the MFD or vice-versa. – Michael C Nov 17 '15 at 0:13