I've picked and read a selection of books written over as wide a date range as I could, to get a sense of how things changed:

The idea that you shouldn't try to pick individual stocks appears to have started to enter popular advice in the early '70s, with "A Random Walk Down Wall Street". By the 1994 "Investing On Your Own" the advice all seems completely what I would expect from a book written now.

Details and quotes:

(Note: when people below talk about "fundamental analysis" or "fundamentalists" they mean predicting future values of stocks based on estimates of the fundamental value of the company, using earnings, growth prospects, etc. When they talk about "technical analysis" or "technicians" they mean predicting from past market activity.)

1888, "The Art of Investing", John Ferguson Hume

He argues that the main focus of the investor should be avoiding junk. For example, on p20 he writes:

Of the securities that are offered with first-class recommendations, it is probable that about one third are actually good, one third have some value, and one third are practically worthless. Hence the very natural inference that whatever art there may be in the matter of investing is to be exercised chiefly in the avoidance of unworthy offerings, and it is to that point that a profitable discussion of the subject must be mainly directed.

He really hates stock exchanges, arguing that they make prices volatile to no benefit. At his most vehement, on p143:

The New York Stock Exchange, which is the soul, the motive power of Wall Street, is an evil in the land, a danger to private wealth, a disturbing force in general business, and a foe to public morals. A not overdrawn descriptions would picture it as an enormous devilfish with a hundred thousand arms, reaching into all parts of the country, and all equipped with suckers more or less powerful, and busy every one of them, in extracting nourishment for the monster to which it belongs.

...

The aggregate tax upon the country for the support of its operations is something enormous. It can not be otherwise when we see how Wall Street lives and flourishes. It maintains a good sized army of operators, the membership of the Stock Exchange numbering nearly twelve hundred—without counting "curbstone" men and other camp followers—who spend with the lavishness of soldiers of fortune, while some of them take unparalleled fortunes out of the street. And yet Wall Street does not produce a dollar. It creates nothing. It draws its sustenance entirely from outsiders. It is a blood sucker.

1912, "How to Invest Money Wisely", John Moody

Full of discussion of railroad stocks and bonds, maybe because those were a large fraction of publically owned companies at the time? Treats the predicting future values as clearly possible: "sell those issues which were quoted clearly above their asset values, and keep those which had the surest potential value for the future" (p71).

Claims conventional advice is:

The kind of advice which is generally regarded as the most conservative for the investor who does not wish to risk his principal is the following: "Think first of your capital and pay no attention to the amount of interest return until the intrinsic value back of the investment has been thoroughly demonstrated. Confine your investments to first mortgages or other successful undertakings which have back of them a heavy earning power and on which the interest has been earned for a long series of years at least three or four times over. Or, select municipal bonds which are backed by the credit of prosperous American cities and about which there is no doubt whatever about the permanent maintenance of high credit. (p12)

and argues that this doesn't work well.

1962, "Pennies and Millions", Dorothy Armbruster

Was VP at the Bank of NY. Argues that it's important to pick the right stocks. For example:

But as long as we have an expanding economy there are gains to be made from investment, if you can know your own situation and your objectives and take pains in selecting the securities you buy—either the old, reliable, well-established stocks or the newer ones which you have thoroughly investigated with expert help. (p151)

1968, "What Every Woman Should Know About Investing Her Money", Herta Levy

Was a broker. Advocates picking individual stocks and gives suggestions (p62-69). Suggests evaluating mutual funds based on past performance:

And the best way I know to judge whether a [mutual] fund meets you objectives is to determine whether or not it has in the past achieved these goals. Has a fund which seeks capital gains demonstrated that it is able to achieve them in the past? Has a fund whose objective is income provided a good return on its investments in the past? (p96)

No one would write this now:

Members of the female sex normally respond to problems of money management in different ways. There is that rare woman who is both thoroughly feminine and thoroughly knowledgeable in financial matters—the one attribute does not interfere with the other. This woman has complete regard and respect for her financial counselors, yet makes her own decisions on the use of her money—based, of course, on sound advice and information. She moves knowingly through the investment world, yet manages to be completely feminine and charming.

Another type of woman is totally out of touch with the money world. Her lack of understanding of matters financial is almost alarming. She may be well educated—up on the theater, literature, art—have the last word on raising children or decorating her home—but this woman's knowlege centers around spending. When faced with investment decisions, this woman would buy stock in Sara Lee because its cake tastes good—sell American Airlines because her last flight was delayed—hang onto a stock for dear life because it was given to her as a wedding present. Such women fail to grasp the fundamentals of investing.

Any reasonably intelligent woman can learn her way around the money world and at the same time preserve her feminine nature. In so doing, she can achieve not only greater financial security but greater emotional security. She will become a more interesting companion for the intelligent men and women around her. (p11)

1972, "The Art of Investing", Philip Lohman

Treats the goal of investment as choosing the right stocks:

Not all stocks will double in value between now [1972] and 1982 as the economy doubles in size. Some will do a lot better than others. The trick is to find out which ones. That is pure art, combined with some scientific reasoning. (p6)

1973, "A Random Walk Down Wall Street", Burton Malkiel

Influential book with a good Wikipedia summary. Popularizes recent academic research and arguments around the efficient market hypothesis. Argues against picking individual stocks, advocates creation of index funds.

1978, "Guide to Intelligent Investing", Cohen et. al.

Nearly the whole book is details on forecasting techniques and other ways of picking stocks, but then in a chapter at the end they present random walk theory and say "the notion that sound investing only means picking 'good' stocks and avoiding 'bad' stocks is fading." (p306) They sum up with "Thus the random walk theory presents an important challenge to investors following the fundamental or technical techniques described in previous chapters." (p314)

1981, "How to Buy Money", Wayne Nelson

Merryl Lynch VP. Treats it as obvious that we can predict stock movements:

Many fundamentalists will argue that you should buy a good stock and cling to it forever. The reasons this doesn't make sense are many. Consider the Dow Jones Industrial Average stocks for a few of those reasons. Assume that you bought these stocks in 1961 and held them over the past twenty year period. Surely there were opportunities to trade out of these stocks at profits, buy them back, and ride them awhile again. There is simply no sense in riding the roller coaster both ways. You should try to get out somewhere close to the top and climb on near the bottom. Take advantage of the cyclical nature of the market. (p110)

Seems to be confused about what the random walk theory claims:

There is a theory called "random walk" which, in essence, says that you're as likely to pick a winning stock by randomly selecting stocks from the pages of the newspaper as by doing the analysis that high priced securities researchers perform. This theory has validity, and you can apply it by making your purchases of common stocks after a trend up or down has been confirmed, rather than in anticipation of a turn.

1983, "Why Stocks Go Up (and Down)", William Pike

All on how to choose the right stocks and value companies. No mention of random walks, efficient markets, or index funds.

1986, "Every Woman's Guide to Profitable Investing", Elizabeth Fowler

NYT Reporter. Generally believes brokers can help you pick stocks that will do better than average.

No analyst can guarantee a company's growth rate, but generally he will be able to make an informal prediction. This is his job, essentially—the msot important job he can do for you, I think, except provide information as to when you should sell a stock. (Here, I believe, many analysts fall down. They are good at forecasting growth, but are often too slow with sell recommendations.) (p65)

And:

If you are a new investor you probably want advice on specific stocks, on market techniques, as well as proper timing. ... An effective broker would keep you from buying IBM shares at their high point. Yield to his experience. He has a feel for the market, based on experience, which (at the beginning at least) you do not. (p77)

1994, "Investing On Your Own", Deborah Rankin

Everything is pretty standard modern investment advice, index funds and all.