If you're building a really quick and dirty demo that you have no intention of extending later, spring can result in a lot of additional configuration issues (not really if you've done it before, but I always end up fighting with it one way or another), so that might be a time to consider just using plain old servlets. Generally though, anything beyond just a super fast and dirty demo, using some form of MVC framework is going to make life in the future a lot easier and is also in line with best practices. Spring makes things super easy, just have to spend some time on the front end configuring everything.
I should note, there's nothing you can do with java servlets that you can't do with Spring. The big difference is setup time.
Edit: It's worth noting that when I posted this answer, I was unaware of Spring Boot that is actually quite easy to get up an running using either an embedded web server or a more conventional web container. Here's a link to a quick start example: http://projects.spring.io/spring-boot/#quick-start
