There are a few great answers already, and I think it is clear that it truly depends on your product, the marketplace and whom you are giving the exclusivity to.
My current company did a big Kickstarter for a consumer kitchen electronics item, and validated a market that didn't quite exist before. We then had an exclusive US launch with a major cookware retailer. It has been a fantastic journey and here are the reasons.
1. Brand exposure: Our brand was new and unknown to the consumers. However, with this major retailer's backing, having retail space at over 100 stores and being included in their catalogs, our brand was validated by their brand image. We could not have bought this level of exposure and validation.
2. Operation expertise: This retailer understood our limitation as a startup, and was kind enough to effectively handhold our company along the way for a while, so we could get our act together on the operation front. It helped us get ready to take on many other major retailers around the world. Mind you, doing physical goods require a lot more logistics setup, and it is no small feat.
3. Marketing: With this retailer's validation, we got even more press because we were now widely available at a store existing in all States. They also helped provide us with data on the success/failure of any campaigns we worked on. Negotiate for this.
4. No limit on other expansion: This exclusivity was limited geographically, so as we learn from working with a major, other international distributor/retailers took note, and we were able to engage them as well. Having a large retailer works with you first, gives other retailers confidence that you know what you are doing. The deal was also limited in time, of course.
5. Sales volume and sales prediction: Obviously, with a relationship like this, we did achieve some good sales volume. Now, startups struggle with cash flow, and with the sales volume, this retailer was able to give us long term forecast, so we could (at least) do some planning with our cash flow. Negotiate for this.
6. Learning: Let's just say that the amount of learning was immense, and fantastic. Money can't buy this.
With that, yes, exclusivity can be a fantastic thing.
Make sure you are also aware of the exclusivity's limits, and make sure that both sides are clear about expectations and have fall back plans. The comment about not putting all eggs in one basket is also accurate. We are fairly balanced on that because we were also developing good sales in other geographic areas and other channels, and we ensured that even if this fell through (the chance of that for us was very low), we would not tank.
This was, of course, a unique case out of many other cases out there. What I want to point out is that exclusivity, when used right, for the right product and with the right partners, can be a good path.