Base View Models
Base view models become god classes which end up being huge monstrosities. What happens is every widget that has to appear on every page ends up being in the base view model. Think of CNN.com or even Stackoverflow.com. You end up with a beast that touches so many different parts of the app. Even SO's case the base view model would have ads, related, login, messages, job ads, links. Thats pretty meaty.
The alternatives are messy, using the ViewData dictionary like a global variable or RenderAction/RenderPartial, but you avoid having your entire app being coupled to your base view model.
Heavy Base Controllers
Base Controllers also have a tendency to become heavy and tightly coupled to a lot of pieces. Most of the time code you throw in your base controller should be in its own action attribute.
Not Exploring MVC Contrib
MVC Contrib is an unbelievable awesome resource for solving common MVC problems. Even simply looking over MVC Contrib will give you tons of ideas and techniques that make developing MVC sites easier.