The only way to know this for sure is to update the version of the Spring dependencies in your project and see whether it compiles. If it does, then that's a good step forward. However, under the hood Spring uses specific versions for pretty much everything (like Hibernate, as the others are also saying), so the next step would be to actually run the web application on a Tridion stack to see what breaks.
In general, Spring tends to be compatible between minor versions. So, the 3.X version should be able to be used up until the latest minor version, which at the time of writing is Spring 3.2.14 of the Spring version 3 branch. That in turn should work with Tridion 2013 and Hibernate 4.1.
Going a major version up (so, Spring version 4.x) will probably be more problematic, as quite a lot of interface definitions will have changed, let alone actual functionality. Again, you can try this out, but personally I see it as a waste of time, if you have full control over your dependency management.
More information on Spring compatibility can be found here: