I recently discovered this one. It is a kickstarter for an anime called "Under the Dog". While they have plans in the works to make a 26 episode series, they are currently looking for funds for a 24 minute pilot episode.
What got me interested is the part of them trying to explain the difficulty in producing new anime these days. While the costs of producing anime is as expensive as ever, what hurts these days is how difficult it is to recoup costs (let alone make a small profit). The money doesn't appear to be there anymore. These days, the person (or people) who creates the copyright almost always have to get a production committee, a committee that helps share costs so no single person or company has to take on the whole risk. The downside is that the people who created the copyright tends to lose a great deal of control over it, and bring on the risk the committee might not work well.
I did some looking and found a good overview (a 3 parter) of some of the problems they face:
If you are interested in backing an anime that does not need to cater to a committee, try to sell a product, or make changes because a committee said so, then maybe you should check it out.