It really is quite remarkable how often this question is asked, and how much misinformation is asserted in response. If the question is about recreational flight, currently regulated by 14 CFR Part 101 subpart E, the rules are clear. This is Part 101 subpart E in its entirety:
Subpart E—Special Rule for Model Aircraft
Source: Docket FAA-2015-0150, Amdt. 101-9, 81 FR 42208, June 28, 2016, unless otherwise noted.
§101.41 Applicability.
This subpart prescribes rules governing the operation of a model aircraft (or an aircraft being developed as a model aircraft) that meets all of the following conditions as set forth in section 336 of Public Law 112-95:
(a) The aircraft is flown strictly for hobby or recreational use;
(b) The aircraft is operated in accordance with a community-based set of safety guidelines and within the programming of a nationwide community-based organization;
(c) The aircraft is limited to not more than 55 pounds unless otherwise certified through a design, construction, inspection, flight test, and operational safety program administered by a community-based organization;
(d) The aircraft is operated in a manner that does not interfere with and gives way to any manned aircraft; and
(e) When flown within 5 miles of an airport, the operator of the aircraft provides the airport operator and the airport air traffic control tower (when an air traffic facility is located at the airport) with prior notice of the operation.
§101.43 Endangering the safety of the National Airspace System.
No person may operate model aircraft so as to endanger the safety of the national airspace system.
There is no altitude limit included, but 101.41 (b) states that "
the aircraft is operated in accordance with a community-based set of safety guidelines and within the programming of a nationwide community-based organization".
Currently that means, effectively, the AMA. If you look at the
AMA Safety Handbook, it has no general altitude limit, but mentions staying under 400 ft within 3 miles of airports. This exact question was raised by the AMA with the FAA, who provided a
written response confirming that there is no altitude limit for recreational flight. That's the law - and supersedes all recommendations and pleas by the FAA on their website.
Looking ahead, in Section 349 of the FAA Reauthorization Act of 2018, which repeals the Special Rule for Model Aircraft that prevented the FAA from regulating recreational flight, the following provision has been added:
In Class G airspace, the aircraft is flown from the surface to not more than 400 feet above ground level and complies with all airspace restrictions and prohibitions.
However, until that is implemented by the FAA in 14 CFR, it does not apply.