A wide variety of other states support initiatives or popular referenda:

Oregon

Oregon very clearly spells out the rules for initiatives and referenda.

Article IV, Section 1:

Legislative Power; Initiative and Referendum

(1) The legislative power of the state, except for the initiative and referendum powers reserved to the people, is vested in a Legislative Assembly, consisting of a Senate and a House of Representatives.

(2)(a) The people reserve to themselves the initiative power, which is to propose laws and amendments to the Constitution and enact or reject them at an election independently of the Legislative Assembly.

(b) An initiative law may be proposed only by a petition signed by a number of qualified voters equal to six percent of the total number of votes cast for all candidates for Governor at the election at which a Governor was elected for a term of four years next preceding the filing of the petition.

(c) An initiative amendment to the Constitution may be proposed only by a petition signed by a number of qualified voters equal to eight percent of the total number of votes cast for all candidates for Governor at the election at which a Governor was elected for a term of four years next preceding the filing of the petition.

(d) An initiative petition shall include the full text of the proposed law or amendment to the Constitution. A proposed law or amendment to the Constitution shall embrace one subject only and matters properly connected therewith.

(e) An initiative petition shall be filed not less than four months before the election at which the proposed law or amendment to the Constitution is to be voted upon.

(3)(a) The people reserve to themselves the referendum power, which is to approve or reject at an election any Act, or part thereof, of the Legislative Assembly that does not become effective earlier than 90 days after the end of the session at which the Act is passed.

California

California has had initiatives since 1911, when it became the tenth state to adapt it.  According to Ballotpedia, “Through November 2014, 364 initiatives have qualified for the statewide California ballot. Voters have approved 123, an approval rate of 34 percent. From 1911 through November 2014, the California Constitution has been amended 52 times through the state’s initiative process.”

 

The California Constitution features this language on initiatives:

Article II, Section 8:

(a) The initiative is the power of the electors to propose statutes and amendments to the Constitution and to adopt or reject them.

(b) An initiative measure may be proposed by presenting to the Secretary of State a petition that sets forth the text of the proposed statute or amendment to the Constitution and is certified to have been signed by electors equal in number to 5 percent in the case of a statute, and 8 percent in the case of an amendment to the Constitution, of the votes for all candidates for Governor at the last gubernatorial election.

(c) The Secretary of State shall then submit the measure at the next general election held at least 131 days after it qualifies or at any special statewide election held prior to that general election. The Governor may call a special statewide election for the measure.

(d) An initiative measure embracing more than one subject may not be submitted to the electors or have any effect.

https://ballotpedia.org/Article_II,_California_Constitution#Section_8

Colorado

The relevant section of the Colorado Constitution is the following:

Article V, Section 1

(2) The first power hereby reserved by the people is the initiative, and signatures by registered electors in an amount equal to at least five percent of the total number of votes cast for all candidates for the office of secretary of state at the previous general election shall be required to propose any measure by petition, and every such petition shall include the full text of the measure so proposed. Initiative petitions for state legislation and amendments to the constitution, in such form as may be prescribed pursuant to law, shall be addressed to and filed with the secretary of state at least three months before the general election at which they are to be voted upon.

(2.5) In order to make it more difficult to amend this constitution, a petition for an initiated constitutional amendment shall be signed by registered electors who reside in each state senate district in Colorado in an amount equal to at least two percent of the total registered electors in the senate district provided that the total number of signatures of registered electors on the petition shall at least equal the number of signatures required by subsection (2) of this section. For purposes of this subsection (2.5), the number and boundaries of the senate districts and the number of registered electors in the senate districts shall be those in effect at the time the form of the petition has been approved for circulation as provided by law.

Chart from The National Conference of State Legislatures