Do you need a special charger for a Nexus 7? I've been trying to use the same charger as I use for my Android phone and it works poorly. If you tilt the tablet upwards it's charging, but otherwise it's not. What's the deal with these Android tablets?
No, you don't need anything unique. While it comes with something specific - it can charge off a USB in your computer (or the wall outlet -> USB). (Source: I have the 2012 one)
Sounds like you have other issues such as:
Bad/Obstructed USB header - Visually check the USB on your Nexus for physical damage or blocks (dust, debris, lint, etc)
Bad USB cable - Try an alternative cable or verify that cable in other devices if possible.
There are complaints of the 2013 Nexus 7, mostly related to odd behaviors with touch. Perhaps this could be another manifestation... Though I somewhat doubt it.
If you clarify further, that may help your cause: Did it ever work normally - if so, has anything changed between then and now (rooting, custom ROM, etc)? What came in the box with it? What did the manual tell you? What else have you tried? What do you mean "What's the deal with these android tablets?" - have you found other evidence of issues or reported complaints?