This turned out be a lot longer than I expected. So, here's the overview.
Despite the presence of asset allocation calculators and what not, this is a subjective matter. Only you know how much risk you are willing to take. You seem to be aware of one rule of thumb, namely that with a longer investing horizon you can stand to take on more risk. However, how much risk you should take is subject to your own risk aversion. Honestly, the best way to answer your questions is to educate yourself about the individual topics. There are just too many variables to provide neat, concise answers to such a broad question. There are no easy ways around this. You should not blindly rely on the opinions of others, but rather use your own judgment to asses their advice.
Some of the links I provide in the main text:
S&P 500: Total and Inflation-Adjusted Historical Returns
10-year index fund returns
The Motley Fool
Disclaimer: These are the opinions of an enthusiastic amateur.
The "essay" itself
Why should I invest 20% in domestic large cap and 10% in developing markets instead of 10% in domestic large cap and 20% in developing markets? Should I invest in REITs? Why or why not?
Simply put, developing markets are very risky. Even if you have a long investment horizon, you should pace yourself and not take on too much risk. How much is "too much" is ultimately subjective. Specific to why 10% in developing vs 20% in large cap, it is probably because 10% seems like a reasonable amount of your total portfolio to gamble. Another way to look at this is to consider that 10% as gone, because it is invested in very risky markets. So, if you're willing to take a 20% haircut, then by all means do that. However, realize that you may be throwing 1/5 of your money out the window.
Meanwhile, REITs can be quite risky as investing in the real estate market itself can be quite risky. One reason is that the assets are very much fixed in place and thus can not be liquidated in the same way as other assets. Thus, you are subject to the vicissitudes of a relatively small market. Another issue is the large capital outlays required for most commercial building projects, thus typically requiring quite a bit of credit and risk. Another way to put it: Donald Trump made his name in real estate, but it was (and still is) a very bumpy ride. Yet another way to put it: you have to build it before they will come and there is no guarantee that they will like what you built.
What mutual funds or index funds should I investigate to implement these strategies?
I would generally avoid actively managed mutual funds, due to the expenses. They can seriously eat into the returns. There is a reason that the most mutual funds compare themselves to the Lipper average instead of something like the S&P 500. All of those costs involved in managing a mutual fund (teams of people and trading costs) tend to weigh down on them quite heavily. As the Motley Fool expounded on years ago, if you can not do better than the S&P 500, you should save yourself the headaches and simply invest in an S&P 500 index fund.
That said, depending on your skill (and luck) picking stocks (or even funds), you may very well have been able to beat the S&P 500 over the past 10 years. Of course, you may have also done a whole lot worse. This article discusses the performance of the S&P 500 over the past 60 years. As you can see, the past 10 years have been a very bumpy ride yielding in a negative return. Again, keep in mind that you could have done much worse with other investments.
That site, Simple Stock Investing may be a good place to start educating yourself. I am not familiar with the site, so do not take this as an endorsement. A quick once-over of the material on the site leads me to believe that it may provide a good bit of information in readily digestible forms. The Motley Fool was a favorite site of mine in the past for the individual investor. However, they seem to have turned to the dark side, charging for much of their advice. That said, it may still be a good place to get started. You may also decide that it is worth paying for their advice.
This blog post, though dated, compares some Vanguard index funds and is a light introduction into the contrarian view of investing. Simply put, this view holds that one should not be a lemming following the crowd, rather one should do the opposite of what everyone else is doing. One strong argument in favor of this view is the fact that as more people pile onto an investing strategy or into a particular market, the yields thin out and the risk of a correction (i.e. a downturn) increases.
In the worst case, this leads to a bubble, which corrects itself suddenly (or "pops" thus the term "bubble") leading to quite a bit of pain for the unprepared participants. An unprepared participant is one who is not hedged properly. Basically, this means they were not invested in other markets/strategies that would increase in yield as a result of the event that caused the bubble to pop.
Note that the recent housing bubble and resulting credit crunch beat quite heavily on the both the stock and bond markets. So, the easy hedge for stocks being bonds did not necessarily work out so well. This makes sense, as the housing bubble burst due to concerns over easy credit.
Unfortunately, I don't have any good resources on hand that may provide starting points or discuss the various investing strategies. I must admit that I am turning my interests back to investing after a hiatus.
As I stated, I used to really like the Motley Fool, but now I am somewhat suspicious of them. The main reason is the fact that as they were exploring alternatives to advertising driven revenue for their site, they promised to always have free resources available for those unwilling to pay for their advice. A cursory review of their site does show a decent amount of general investing information, so take these words with a grain of salt. (Another reason I am suspicious of them is the fact that they "spammed" me with lots of enticements to pay for their advice which seemed just like the type of advice they spoke against.)
Anyway, time to put the soapbox away. As I do that though, I should explain the reason for this soapboxing. Simply put, investing is a risky endeavor, any way you slice it. You can never eliminate risk, you can only hope to reduce it to an acceptable level. What is acceptable is subject to your situation and to the magnitude of your risk aversion. Ultimately, it is rather subjective and you should not blindly follow someone else's opinion (professional or otherwise). Point being, use your judgment to evaluate anything you read about investing.
If it sounds too good to be true, it probably is. If someone purports to have some strategy for guaranteed (steady) returns, be very suspicious of it. (Read up on the Bernard Madoff scandal.) If someone is putting on a heavy sales pitch, be weary.
Be especially suspicious of anyone asking you to pay for their advice before giving you any solid understanding of their strategy. Sure, many people want to get paid for their advice in some way (in fact, I am getting "paid" with reputation on this site). However, if they take the sketchy approach of a slimy salesmen, they are likely making more money from selling their strategy, than they are from the advice itself. Most likely, if they were getting outsized returns from their strategy they would keep quiet about it and continue using it themselves. As stated before, the more people pile onto a strategy, the smaller the returns. The typical model for selling is to make money from the sale. When the item being sold is an intangible good, your risk as a buyer increases.
You may wonder why I have written at length without much discussion of asset allocation. One reason is that I am still a relative neophyte and have a mostly high level understanding of the various strategies. While I feel confident enough in my understanding for my own purposes, I do not necessarily feel confident creating an asset allocation strategy for someone else. The more important reason is that this is a subjective matter with a lot of variables to consider. If you want a quick and simple answer, I am afraid you will be disappointed. The best approach is to educate yourself and make these decisions for yourself. Hence, my attempt to educate you as best as I can at this point in time.
Personally, I suggest you do what I did. Start reading the Wall Street Journal every day. (An acceptable substitute may be the business section of the New York Times.) At first you will be overwhelmed with information, but in the long run it will pay off. Another good piece of advice is to be patient and not rush into investing.
If you are in a hurry to determine how you should invest in a 401(k) or other such investment vehicle due to a desire to take advantage of an employer's matching funds, then I would place my money in an S&P 500 index fund. I would also explore placing some of that money into broad index funds from other regions of the globe. The reason for broad index funds is to provide some protection from the normal fluctuations and to reduce the risk of a sudden downturn causing you a lot pain while you determine the best approach for yourself. In this scenario, think more about capital preservation and hedging against inflation then about "beating" the market.