"One hundred and thirty-five" is perfectly correct, although the "and" tends to be removed in American English. It makes sense mathematically, since "and" is synonymous with "plus" — two apples and three apples makes five apples. One hundred, and thirty-five, makes 135.
The "and" is particularly useful when articulating a series of numbers. "One hundred one, one hundred two" could easily be misheard as "one hundred, one, one hundred, two" whereas using "one hundred and one, one hundred and two" removes that ambiguity.
Ultimately though it depends on location and culture. In the UK the "and" is always used; in the US there are a mixture of usages.
Looking at this ngram, it seems that skipping the "and" has only gained popularity over the last hundred years or so but using the "and" is still far more prevalent:
To investigate this question via Google Books, I ran searches for a small subset of potential matches: "but as much as," "but much as," "and as much as" and "and much as." My goal was simply to look at what these "core samples" (to use a geological term) turned up, and to see whether the results supported any larger inferences about the relative age of the concessive "as much as" versus the concessive "much as."
The earliest match for a concessive "but as much as" in a Google Books search appears in Edward Stillingfleet, Origines Britannicae, or The Antiquities of the British Churches (1685):
But, as much as this looks like a Monkish Legend, Alford and Cressy are much displeased with Sir H. Spelman for calling it in question.
The next-earliest match is in Peter Pett, The Happy Future State of England (1688):
But as much as it is the inclination of the unthinking or brutish part of Mankind, that power should be like the Crocodile alwaies growing, the soberer few do know, that power will destroy it self if it shall be still ascending and hath not a Center wherein to rest and be quiet, just as a fire would perish in nature and destroy it self, if there were not an Element allow'd it wherein to leave burning :
A couple of fairly early instances come from very prominent authors. From Richard Steele, The Tatler, No. 48 (July 30, 1709):
But as much as I was curious to observe the Reception these Gentlemen met with upon Change, I could not help being interrupted by one that came up towards us, to whom every Body made their Compliments.
From Daniel Defoe, The Fortunate Mistress (1724):
But as much as I was hardened, and that was as much as I believe ever any wicked creature was, yet I could not help it, there was and would be hours of intervals and of dark reflections which came involuntarily in, and thrust in sighs into the middle of all my songs ; and there would be sometimes a heaviness of heart which intermingled itself with all my joy, and which would often fetch a tear from my eye.
The first match for a concessive "but much as" in the Google Books search results is from "Summary of Proceedings in the present Session of Parliament, Thursday, Feb. 17," in The Gentlemen's Magazine and Historical Chronicle (April 1785):
These he considered as insignia of notable services tendered by the patentees for the advantage of the state; but, much as he respected patent interests, he would not go so far as to admit, that the patentees had a right to consider the enormous unforeseen accumulation of profit arising from the distresses of their country as a property sacred, which no reform was ever to touch.
The phrase "and as much as" used concessively first appears in a Google Books match from William Sherlock, "A Sermon Preach'd at St. Paul's Cathedral, November 22, 1699" (1699):
And as much as some Smile at the Conceit , I can't but think, That the General Exhortations in the New Testament, to Sing to God, To admonish one another in Psalms, and Hymns, and Spiritual Songs, Singing and Making Melody in our Hearts to the Lord ; Though they are not an Apostolical Institution of a Quire, nor do prescribe the particular Forms of Cathedral Worship ; yet they justify it all, as far as it I fitted to the True Ends of Devotion ;
Three years later, from Charles Trimnell, "An Answer to a Third Letter to a Clergyman in the Country, in Defence of the Entry of the Parliament-Writ, &c." (1702), we have this:
And as much as you pity my Weakness upon this occasion, you have said nothing to alter my Thoughts, but that if the Entry of the Provincial Writ by it self, much more that of the Parliament, had been reputed necessary according to custom ; this Forma wou'd have directed the Exhibition of them.
The first match for a concessive "and much as" in the Google Books search is from "The Tears of Cambria" (1773):
Yet could I once untir'd have heard thee sing,
And dwelt for ever on the syren string ;
And much as grief has quench' d my thirst of praise,
Ev'n now not proof to such seducing lays,
Rapt with the noble purpose of thy lyre,
Fain would I catch the same congenial fire ;
The first prose example of "and much as" appears in the Google Books search results appears in "Summary of Proceedings in the present Session of Parliament, Tuesday, Jan. 3," in The Gentleman's Magazine (February 1786):
Mr. Pitt rose, to return his thanks to the honourable gentleman, for having so properly brought under the consideration of the house a matter of such truly national importance as the militia ; the interval of peace was undoubtedly the fittest moment possible for them to unite in endeavouring to put that great and most constitutional defence of the kingdom upon a respectable footing ; and, much as he professed himself the friend of oeconomy in that, as in every other branch of the public service, he was not so much a slave of his opinion, as by any means to wish to lesson [sic] the advantages the country had felt from a well-regulated militia ; but, he confessed, he did not entirely think, with the honourable gentleman, that it was so entirely necessary fro the militia to be embodied every year..
To sum up, my Google Books searches for concessive "but as much as" and "and as much as" yielded matches from the late 1600s forward. The corresponding Google Books searches for concessive "but much as" and "and much as" turned up valid matches in prose beginning in 1785 and 1786, respectively—both, coincidentally, from reports of Parliamentary debates—with one earlier poetic occurrence from 1773.
Since my sample is narrowly defined, I can't draw any definitive conclusions, but the search results I obtained certainly suggest that concessive use of "as much as" is considerably older than concessive use of "much as."
Best Answer
I ran Google searches for "one hundred one" and "one hundred and one" for the period 1600–1900. Many of the matches are false positives—but among the valid ones, "one hundred and one" appears more frequently and from a much earlier date.
The earliest match for "one hundred and one" is from the fascinatingly titled An Historical Essay: Endeavoring a Probability That the Language of the Empire of China is the Primitive Language (1669), by "John Webb of Butleigh in the County of Somerset Esquire":
The earliest match for "one hundred and one" preceding a noun is from "Several Clauses in an Act, Intituled, An Act for making good the Deficiencies of several Fonds therein mentioned; and for Enlarging the Capital Stock of the Bank of England ; and for Raising the Publick Credit" enacted in "Anno 8 & 9 Gulielmi III Regis" (that is, in 1697 or 1698), reproduced in The Act of Tonnage and Poundage, and Rates of Merchandize (1702):
The earliest Google Books match for "one hundred one," meanwhile, is from Elias Voster, Arithmetic, in Whole and Broken Numbers, Digested after a New Method, and Chiefly Adapted for the Trade of Ireland, thirteenth Edition (1774):
And the earliest match for "one hundred one" preceding a noun is from a lengthy series of tax tables included in "An act to authorize the Portland Union Railway Company to divide their stock into shares of less than one hundred dollars each" (March 16, 1860), in Acts and Resolves Passed by the Thirty-Ninth Legislature of the State of Maine (1860):
On the evidence of these (and other early) Google Books search results, it appears that "one hundred and one" was in use by the second half of the 1600s and that "one hundred one" was in use by the second half of the 1700s.