I've seen "$.02", "2¢", "just my two cents", etc, similar in meaning to IMHO, except usually appended to the main text.
As the Ngram shows, it is only "two cents" that is popular in this usage:
How does "two cents" express humility of opinion?
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Urban dictionary has some surprisingly good entries on the topic if you ignore the humour surrounding it:
This phrase draws an analogy to the poker ante (two bits) and gains your entry into the conversation.
The trick is recognising the (I assume) older bits instead of cents.
Also, two-bit still lives on in common usage, meaning "insignificant":
That's my insignificant contribution.
Wikipedia has only speculations that it is related to either or both of these sayings:
IMHO the ironical meaning of this phrase is mostly lost on the internet -- "that's my two cents" nowadays just means "that's my opinion, take it or leave it", whereas it once implied self-deprecation, at least according to the eminently fallible urban dictinary. There are lots of British slang phrases (which seem to be mostly 19th century) that include the amount of two pence as a designator of something cheap or worthless (twopenny-rope, two penn'orth of tripe, tuppeny-ha'penny) so maybe "my $.02" is derived from them. As Stan Rogers says above, 2 pence would have been a fairly substantial amount to many people in Victorian times, so I'm a bit confused about this.
The 'two cents' family
The idiom "my two cents" is one of a number of expressions in U.S. English tied to a notion of "two cents" as a paltry or negligible amount. Related expressions include "for two cents," "like two cents," and "[not] worth two cents." Here is the entry for "for two cents" in Christine Ammer, The American Heritage Dictionary of Idioms, second edition (2013):
for two cents For nothing; for a petty sum. For example, For two cents I'd quit the club entirely. Similarly, like two cents means "of little or no value or importance; worthless," as in She made me feel like two cents. The use of two cents in this sense is thought to be derived from a similar British use of twopence or tuppence, which dates from around about 1600. The American coin was substituted in the 1800s, along with two bits, slang for 25 cents and also meaning "a petty sum." Similarly, put in one's two cents or two cents' worth, meaning "to express one's unsolicited opinion for whatever it is worth," dates from the late 1800s.
Early instances of '[one's] two cents [worth]'
An Elephind search of old newspapers in various archives reveals the interesting coincidence that the two earliest matches for "two cents worth" involve the price of a newspaper. From "Can I Help You?" originally printed in the [Boston, Massachusetts] Olive Branch, reprinted in the Huntingdon [Pennsylvania] Globe (November 19, 1856):
But look! yonder comes a broad shouldered, frank-browed man, who meets his poor brother with a hearty slap on the shoulder. and I can I help you?—just say the word—Don't be afraid now; what's your trouble? Out with it, and if you'd like a little cash, just say so. ... He don't clap his hand on his pocket with a styx like frown that says as plainly as if he bawled out in your ear, no entrance here. He is not one of those dyspeptic, cross-grained, surly, monied machines, that squeezes a sixpence till it squeals and reads a newspaper with a greedy, voracious eagerness, for fear he shall not get his two cents worth. He lives for something else that man, than gain.
And from "The Daily Newspaper: How It Is Prepared," in the Sunbury [Pennsylvania] American (November 3, 1866):
Let him [the reader] reflect that all the appliances of art and science, the telegraph, the steam engine, and the printing press, are brought into play to give him information; that editors, reporters, and correspondents all cudgel their brains for his benefit; that, two or three hundred men have worked long and hard in order to give him his two cents' worth, and if he be not convinced, then he deserves to be placed where, he can never more see a newspaper, which of all things in this world is the great civilizer and humanizer of the race.
This, then, is briefly the work for which each individual pays the trifling sum of two or three cents, and if every man who reads this article, is not convinced that he gets his full money's worth, let him take a position, if he can, upon some first-class paper, and learn for himself the amount of absolute toil which is requisite to produce even a single article like this.
These instances involve "two cents worth" in its literal sense. But figurative instances appear by the early 1900s. From "Chimmie's History," in the Washington [D.C.] Times (March 19, 1911):
And they awl put up thare guns, and was jest about to shoot her ["Barber Fritchee"] with reel bullits. when Stone Wall Jack's son put in his two cents worth.
Cut that rite out, he sed. The furst man that toutches her harey old gray hed, he sed, will wish he hadent I'll teetch you to waist bullits, he sed. Forwerd, martch!
From "The Vatican and Peace," in the New-York Tribune (September 17, 1915):
Only a man living in an intellectual backwoods believes to-day that the Catholic Church is engaged in political intrigue. Impartial historians of all shades of belief have disproved many of the traditional lies about her political activities in the past.
If every blatant ass with his or her two cents' worth of knowledge may shout for why must the great Roman Catholic Church keep silent? Has she no interest at stake? Is there none of her children on the battlefield?
From Guy Bolton & Frank Mandel, "The Five Million," in the [New York] Evening World (August 9, 1919):
"Well, gentlemen," admitted Doug, in great embarrassment, "I feel very much the way I did that day I dropped behind the German lines and found myself looking into the business end of a gatling gun."
"Glad to see you know when you're licked," sneered Bert Weaver, maliciously. Otis Weaver turned upon his offspring and roared:
"Who asked you to put in your two cents' worth of opinion? Shut up!"
I couldn't find any instances of "my [or your, our, his, her, or their] two cents" used figuratively to mean "unsolicited opinion" before the three examples cited immediately above. To me, this provides some circumstantial evidence that "my two cent" originated as "my two cents worth [of opinion, commentary, or other contribution to a discussion]."
A side note on 'not worth two cents'
It is also interesting that the expression "not worth two cents" appeared in figurative use at least as early as 1859 in the sense of "of very little account." Thus, for example, from "The Return of Uncle Sam," in the Sacramento [California] Daily Union (February 14, 1859):
The Uncle Sam left our harbor at 7 o'clock yesterday morning, in the face of a strong head wind, which continued to increase in the strength till 10 o'clock at night, when it had become so terrific, and the sea run so high, that it became evident the steamer could not live in it without being relieved of the large amount of freight which encumbered her upper decks and rendered her top heavy. Accordingly, orders were given that all hands should go to work throwing overboard everything on the upper decks, and, as there were 500 men on board, a busy scene was presented, though not all would work. Some were listless and indifferent; others were praying, some swearing, and some said it was of no use to do anything; the vessel must founder; their lives were not worth two cents apiece. The sea was running mountain high, and wave after wave broke over her, to the great peril of all on deck.
From "Travelling in Palestine—A Disgusted Chicagoan," in the Macomb [Illinois] Journal (July 17, 1868):
I know a Bostonian who, after spending three days in the city [of Jerusalem] and two at the Jordan and Dead Sea, hastened back to Jaffa, declaring that the whole country was not worth two cents.
From S. Annie Frost, "Jack and the Bean Stalk," in Godey's Lady's Book and Magazine (February 1871):
Scaredtodeath. You wretched child! How did you come here?
Jack. You'll never guess, so I'll tell you. I came on a bean stalk.
Scaredtodeath. Do you know where you are?
Jack. I have not the faintest idea.
Scaredtodeath. You are where your life is not worth two cents.
And from "Gov. Hampton a Murderer," originally in the Methodist Advocate, reprinted in the [Cleveland, Tennessee] Weekly Herald (June 7, 1877):
Hampton was fierce to execute vengeance on the so-called Lowndesville (colored) rioters. It now turns out that they were simply trying to defend themselves from white murderers and that after a careful examination of the facts Gov. Chamberlain had pardoned them. Of the fifteen charged with riot, five were murdered, three hung by Hampton, and the other seven imprisoned for life. That is the "justice"' which the colored people receive under Mr. Hampton. His promises to the President are not worth two cents a bushel.
As Christine Ammer observes, idiomatic U.S. English expressions using two cents to convey the meaning "a negligible amount" are easy to find as far back as the 1850s. It is noteworthy that in the nineteenth-century United States, two cents was at various times the price of a newspaper, the price of a postage stamp, and the recommended weekly charitable contribution suggested by The Baptist Missionary Magazine. That two cents became synonymous in multiple settings and multiple set phrases with something of small cost or value is not surprising.
The specific phrase that "my two cents" seems to have arisen from is "[one's] two cents worth," an expression implying that the proffered opinion is not worth much as a marketable commodity. Although Ammer says that expressions of the form "put in [one's] two cents" go back to the late 1800s, the earliest such example I could find was from 1911.
My recollection of 'for my two cents' is as a reference to pay toilets, which cost 2 cents.
Therefore it is a reference to 'my opinion, which in your opinion is worthless, cost me 2 cents'; a self-depreciating method to offer your opinion.
It also reminds of the grafitti:
Here I sit all broken-hearted:
paid 2 pence and only farted.