What's so special about the valley, besides being around other startup folks, that entrepenuers feel they must be located there? Now before you go off quoting Paul Graham or Marc Andreessen please consider these folks have a vested (pun?) interest in startups being (or wanting to be) located in SV, and thus their opinions are partially biased (or drunk with kool-aid).
Personally I don't think it does. As a matter of fact, I think being in Silicon Valley can even be a disadvantage for these reasons:
As a bonus answer, what would you consider an ideal alternative to Silicon Valley? Seattle, Austin, Toronto, New York, London, even Boise (google "Boise startup") seem like good alternatives.
Short answer: No.
Long answer: what do you mean by "successful"? Something the valley has that other places can't match is their pr machine that breaks the laws of physics (the amount of energy that comes out of their buzz/gossip system seems to be more than goes in). However there's a lot of noise and it may be hard to get attention if you don't already have a track record and networks.
If you measure success as "get funding" or "make tonnes of money" there may be other options as other communities can help you get there just as well if not better.
Also, you may want to consider places outside of the US. Waterloo, ON for example is one of the best places to launch a startup in North America - the entire community lives and breathes tech and startps, which is pretty cool. There are also top-notch universities (good for finding talent). A couple of organizations & initiatives there to check out: Communitech (www.communitech.ca) and the AcceleratorCentre (www.acceleratorcentre.com). There's also another accelerator for Digital Media startups being built right now. I'd also suggest it's a lot less expensive to run a startup here than in the valley.
Then, again, I'm biased - this is where I chose to launch my startup.
But on the other hand, so did the folks behind the BlackBerry and others.
I think it depends on what you are looking for as to where a good place may be.
For example, in SV there are a large number of people that are very talented, used to the stresses of a start-up and knowledgeable in what may work.
But, as you mentioned, there is also groupthink there, as, like MBAs, they saw what worked somewhere and decide that that is how things should work.
If you don't need that type of culture, and you are just looking for a place that is a hotbed of innovation, you may want to look at the Research Triangle, in North Carolina, as the anchors are three very good universities.
If you are doing a gaming start-up, the state of Georgia is trying to attract indies to work there, and they will be trying to provide assistance.
If you are doing something that will be involving the government then around DC is a good choice as you will find domain experts there, and many start-ups seem to spring up around there, as there is so many high-tech industries there.
There are other places that would be good, but it depends heavily on what type of market you are looking at, what the product is and what you will need to help you get to the next step.
For example, if I wanted to create a new electric car design, then Michigan may be a good choice, as there are a lot of automotive engineers there, so you could start your R&D there then go elsewhere for production, but prototyping there would be a good idea.
Nassim Nicholas Taleb has an interesting perspective on this in The Black Swan. He says you should choose your location to maximize the chance you will benefit from network effects by randomly encountering people/situations that will yield "positive black swans". That is to say: The huge scalable (unforseeable!) benefits expected from random networking are so huge that they far outweigh the known costs of living in a place like Silicon Valley.
I plan to follow this advice in choosing where to live next.
So, It definitely isn't necessary to launch in Silicon Valley, but you should look at the local startup scene and determine what types of startups are being run in the area. For example, starting a Pharma venture in Boston would be your best bet.
Finally, a blog post from Don Dodge identifying the numerous resources available to Boston Startups.
Silicon Valley is an IT "industrial" district such as Detroit used to be for the car making industry long time ago. Usually you go to a district to get the "bonuses" from being there, examples are, as mentioned by Rob Brown, plenty of qualified/smart people, networking, etc...
Nevertheless, you can always start outside the district, but you will not get extra bonuses. I think Fog's Creek (based in NYC) is a nice example of a startup that didn't grow out of the valley.
A nice/suggested reading I'd recommend "The Spatial Economy, Cities, Regions, and International Trade" by Paul Krugman, (quite tough but you might skip to the findings).
If you're trying to raise money, it helps to be in a hub like sillycon valley or NYC/Boston (or maybe a minor place like Austin or Seattle). Because: most investors like to be physically near their companies. Otherwise the question is only: Can you hire the talent you'll need in the next 5 years? Of course you can't really know what's going to be needed in 5 years, so on average you have to ask "Where do talented people occur naturally, and who like to work at startups?"
So "just anywhere" is not an answer, but sillycon valley isn't the only option either. Here, for example, Austin is a fantastic scene of creative, smart people with a great tradition and network for startups. In absolute numbers it's teeny compared to NYC/Boston/Cali, but your own startup isn't about numbers, it's about you.
Don't forget about the $800 minimum franchise tax required for most companies (there is no grace period for most LLCs) in CA.* And the California state budget is spiraling out control -- who knows how state taxes may be "re-adjusted"...
Good ideas above. Be entrepreneurial! Tapping local networks and resources to start a Silicon Valley-like trend in a relatively obscure region you're familiar with may just be the ticket to success. Remember, the internet is supposed to break down geographical barriers, not make them!
*Disclaimer: The above is a general entrepreneurial tip, not legal advice.