It's common practice now, and maybe required for most airlines. But I don't think that earlier pilots made the same announcements that they do today. When did pilots start making in-flight announcements to passengers? And all the announcements sound the same, is there a standard format for making announcements?
This varies by jurisdiction and air frame in question as the brief is usually specific to the air frame. Ill answer for the FAA.
What the pilot needs to say (by law) is governed by (follow link for full text),
(a) Each certificate holder operating a passenger-carrying airplane shall insure that all passengers are orally briefed by the appropriate crewmember as follows:
(1) Before each takeoff, on each of the following:
(i)Smoking. Each passenger shall be briefed on when, where, and under what conditions smoking is prohibited including...
(ii) The location of emergency exits.
(iii) The use of safety belts...
(iv) The location and use of any required emergency flotation means.
(v) On operations that do not use a flight attendant, the following additional information:
(A) The placement of seat backs in an upright position before takeoff and landing.
(B) Location of survival equipment.
(C) If the flight involves operations above 12,000 MSL, the normal and emergency use of oxygen.
(D) Location and operation of fire extinguisher.
(2) After each takeoff, immediately before or immediately after turning the seat belt sign off, an announcement shall be made that passengers should keep their seat belts fastened, while seated, even when the seat belt sign is off.
FAR 121.571 comes off Doc. No. 2033, 30 FR 3206, Mar. 9, 1965 and was presumably added to the regulations in 1965.
Yes there is a standard. You can find more details in this Advisory Circular AC121-24C which covers what the oral brief needs to contain in more depth and outlines the standards. This AC has been in place since 2003 and replaces AC121-24B which took effect in 1999 I cant find the full text of that one so Im not sure what it replaced (presumably AC121-24A).
There is no direct regulation in the FAR's (or current AC) that require announcing things like route, altitude or temp.