Some watercraft are far more stable than others, but no one would suggest ever standing on a kayak even in stable waters. The folks at California-based TrueRec have come up with such a boat that can remain stable for those who wish to stand to fish or just stretch their legs.
The DFP (Dive-Fish-Paddle), which is being developed by TrueRec through a Kickstarter project, is a sit-on-top kayak, but it is notable that it features spring-loaded pontoons that fold out to the sides and provide added stability when stopped. It offers a multi-function cavity that can be used as storage, making this a boat that can haul you and your gear where you need to go.