As a former consultant at the Boston Consulting Group I saw first hand when, from my viewpoint, our team delivered value to the client and when we did not. Across six cases over two years I witnessed the clichéd excesses of management consulting as well as the benefits. Here are some suggestions on when not to hire consultants and when to do so; hopefully useful since such teams cost about $150,000 - $200,000 per week.

When not to hire strategy consultants
Anything to do with strategy
Time and time again I witnessed that consultants can't possibly have a deep understanding of an industry - product tradeoffs, customer's changing preferences, 2nd and 3rd level cost drivers. Consequently they often rephrase and merge various analyst opinions without an original hypothesis. This gets even worse if your industry is immature and/or fast-changing as consultants have even less to base their theories on then.
On one case in 2006 I was to help a client consolidate their data center footprint. I performed a detailed analysis and both my partner and the client loved my recommendations. Indeed, I got my highest rating ever on a case here. Shortly thereafter I left to join Sungard Availability Services where I ran their data center portfolio of 35 sites with 4M sq. ft. After a year at Sungard I realized that my recommendations in the case at BCG were wrong and missed two key drivers: that power utilization was far more important than real estate utilization and that cloud computing was reducing the need for co-located sites.
Both of these points have $30M-$50M ramifications on data center buildouts and I missed that. I reflected for years on how the client could have let me get away with these erroneous conclusions, given they must have known data centers better than I did. My client appeared smart so I don't think he was fooled somehow. My only theory is that they never cared for my exact conclusions and this was a case of needing the consulting stamp of approval.
Proving your viewpoint to management
As my last example suggests, this one is a sad reality in two senses of the word. That a client feels they need the "independent" stamp of approval from a management consultant (maybe at the behest of their board) and that consultants are willing to charge an exorbidant fee for such "analysis". Every consulting firm will say they start with a clean sheet of paper, without specific conclusions in mind, but I don't think that's always true, if ever really.
I once did a case to help the client figure out branding after they acquired three companies that they were going to merge. The conclusion was obvious a week into the case but we pressed on, for five more weeks, to certify the conclusion somehow. The client though remained happy and sure enough, got their recommendation on the branding outcome after we finished our case.
When to hire strategy consultants
Emergency horsepower, particularly for data analysis
Primary research within your industry
Where do strategy consulting firms go from here
Strategy consulting came of age in the 1950s when most clients did not have broadly competent management teams with training in economics and finance. An MBA on a management team was rare. Today, most companies in the US are crawling with MBAs and, particularly at the management level of leading firms, ex-strategy consultants abound. Consultants simply cannot peddle cost analysis or market research as services worth $200k/week anymore to their own bretheren. With the recent collapse of Michael Porter's Monitor Consulting Group, I suspect the strategy consulting industry will go through a contraction in North America at least; not sure if consulting firms are ready for this.