Lack of UI a feature: proceed carefully and implement immutable statistics
I think there is some movement on this board to give users more control over deleting or editing goals, but I wanted to point out that your current lack of an interface for these things is actually a bit of a feature. It makes you think twice about what goals you create (commit to). For instance, I have a dud email goal hanging around, I set it to end in a week and I hope it goes away, but as an end-user I don't know if it will and it makes me more careful about creating goals I don't want or failing at goals that will stare at me. So, if/when you implement a more robust interface for creating, deleting, and modifying goals, please keep in mind the merit of this stickiness in both increasing my commitment and enhancing the filter with which I judge my priorities. I would recommend that with such an interface, also keep immutable account statistics--number of goals created uncommitted, the number of goals failed, etc. If not completely immutable, make it all or nothing, "Are you sure you want to delete ALL of your history? Success history will be lost too!" This long-term accountability will help as much as the short-term accountability of specific goals.
Admittedly, this idea is not clear cut or well refined. Please vote me up if you agree on the general notion, and argue the details in the comments.

We’re still thinking hard about this. Thanks so much for the insight here — it definitely cast this issue in a new light for us.
Here’s the link to the feedback page about deleting goals: http://beeminder.uservoice.com/forums/3011-general/suggestions/2353108-let-us-delete-goals
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Admindreeves (Cofounder, Beeminder) commented
We've done a few things in the meantime to try to strike the right balance between these schools of thought:
1. When you create a goal you can mark it as ephemeral, pre-specifying that it's just for testing and you don't want it to stick around.
2. You can "archive" goals, shoving them below the fold on your gallery page.
3. If you painstakingly delete all the data points then the option to delete the graph will appear.