First, keep in mind that the Turnpike and the MDC are special. They get to make their own rules (see MGL 81A-4, MGL 92-37). Except where noted, none of the following applies on the Turnpike or MDC roads.
Chapter 90, section 17 of the Massachusetts General Laws begins:
No person operating a motor vehicle on any way shall run it at
a rate of speed greater than is reasonable and proper
This is the "basic rule". It applies on all public roads in Massachusetts,
including the Turnpike (see MGL 81A-20)
and MDC parkways, and all states have substantially similar laws.
Section 17 continues to say the following are prima facie evidence of unreasonable speed:
"Prima facie" evidence means that you can be convicted of speeding if you exceed these speeds and no additional evidence is required, but you are allowed to present evidence that your speed was reasonable. In most other states, speed limits are absolute; you are breaking the law by exceeding the speed limit regardless of whether you are driving safely.
Section 18 sets the standards for posted speed limits. All posted speed limits must comply with section 18, even those that are the same as a section 17 unposted limit. There is actually a difference between unposted 30 and posted 30: you are not speeding until you exceed 30 MPH for 1/8 mile if no limit is posted (40 for 1/4 mile outside of a thickly settled area).
An entity in control of a highway must adopt a speed regulation and have that regulation approved by the state government (Highway Department and Registry of Motor Vehicles) before the limit can be posted. This is important, because unlike some states it is the regulation that matters, not the sign. The official policy of the Highway Department is not to approve any speed limit that does not comply with its speed zoning manual, and the department will generally do some investigation of its own to make sure the proposed limit is reasonable.
The goal of most cities and towns is to get the smallest possible number on the sign. They don't have to approve a speed limit on a road if they don't like it, and they will generally not approve limits higher than the unposted limits. For example, the Highway Department recommended a 35 MPH speed limit on Concord Avenue in Belmont. But 35 is greater than 30, so the town didn't accept it.
MassHighway has more flexibility on its own roads -- they only need the Registrar's approval.
The speed limit is currently set by law at 65 on about half of the Turnpike. According to Turnpike regulations (730 CMR 7.08(6)(c)) limits are (unless posted lower)
Since 1966 traffic control devices (such as speed limit signs) on public roads have been required to comply with the Manual On Uniform Traffic Control Devices. MUTCD section 2B-13 requires that a speed limit sign show the limit established by law or regulation, and additionally requires that the speed limit be based on an engineering study. The MUTCD has legal force through Federal Department of Transportation Regulations (23 CFR 655) as well as MGL 85-2.