Yes, Teespring is a legitimate business, not a scam. It has raised over $60M from top Silicon Valley venture firms such as Andreessen Horowitz and Khosla Ventures. It was also awarded the #1 Product of the Day on Product Hunt on December 23, 2013.
The company started by making it easy to design and sell custom t-shirts. Their "secret sauce" was handling all of the heavy-lifting in terms of inventory, marketing, and logistics, so that anyone could sell custom tees. They have since expanded their social commerce offering to allow their customers to design, market, and sell custom merchandise of all kinds.
Mentioned in this answer
Teespring Direct
Simple high-quality swag for you or your company