This idea is inspired by this question.
Suppose the OP decides to fly some kites or helium balloons above his farm to keep other pilots from flying near it. Regulation-wise, how high can these objects go?
It depends how big the balloon or kite is. Balloons and kites are governed by 14 CFR 101, but specific regulations only apply above a certain size. 101.1 says:
a) This part prescribes rules governing the operation in the United States, of the following:
(1) Except as provided for in §101.7, any balloon that is moored to the surface of the earth or an object thereon and that has a diameter of more than 6 feet or a gas capacity of more than 115 cubic feet.
(2) Except as provided for in §101.7, any kite that weighs more than 5 pounds and is intended to be flown at the end of a rope or cable.
However, note the reference to 101.7, which says (in part):
No person may operate any moored balloon, kite, amateur rocket, or unmanned free balloon in a manner that creates a hazard to other persons, or their property.
That means, if your balloon or kite is too small to be governed by part 101 then there are no specific restrictions on how you operate it, but you still can't fly it in a way that puts other people in danger.
If part 101 does apply to you, then you have to follow the rules in 101.13 and 101.15:
§101.13 Operating limitations. (a) Except as provided in paragraph (b) of this section, no person may operate a moored balloon or kite—
(1) Less than 500 feet from the base of any cloud;
(2) More than 500 feet above the surface of the earth;
(3) From an area where the ground visibility is less than three miles; or
(4) Within five miles of the boundary of any airport.
(b) Paragraph (a) of this section does not apply to the operation of a balloon or kite below the top of any structure and within 250 feet of it, if that shielded operation does not obscure any lighting on the structure.
§101.15 Notice requirements. No person may operate an unshielded moored balloon or kite more than 150 feet above the surface of the earth unless, at least 24 hours before beginning the operation, he gives the following information to the FAA ATC facility that is nearest to the place of intended operation: [contact details, time, altitude etc.]
There are more requirements in 101.17 and 101.19.
As the Internet is a World wide communication medium, it should be noted what country's rules are being quoted. In Australia the rules for recreation aviation activities is governed by CASA (Civil Aviation Safety Authority). The general rule is 120 metres or 400 ft. AGL. and not within 5 km of airports and requires apecial approval with a zone and conditions assigned. 400 ft. is nearly out of sight for a small kite and is a pain to wind that much line in for a child. Adults may fly bigger kites and they may occasionally exceed these limits and brag about it on forums. They often don't know the regulations or don't care. Generally flying a kite at 500 or 600 ft. doesn't cause problems to air traffic as long as it's not near an airport. The normal low level cruise for light aircraft is 1,500 ft. so it is not that easy to a fly a kite that high and consequently I would say it is very rare that a pilot would encounter a kite. People seem to fly kites almost exclusively at kite festivals or the beach these days. I know these things because my team captured the World Record of 16,009 ft. in 2014.