Make it so that's impossible to actually release anything without fixing the tests.
- Fail the build if any tests fail.
- Fail the build if any tests are ignored.
- Fail the build if test coverage goes below a certain level (so people can't just delete tests to work around it).
- Use the CI server to do your release builds, and only allow builds from the server's build drop to be promoted to UAT/staging/production/whatever.
The fact of the matter is, if your build is broken for more than about 15 minutes at a time (and that includes failing tests), then you aren't doing continuous integration.
The "nuclear option" is to have your source control server refuse commits/checkins from any user other than the one who broke the build. Obviously an admin needs to be able to override this temporarily if said person goes on holiday - but, if everybody knows that the whole team is screwed until they fix their tests, then they'll resolve it damn quick.
A good policy (which is even better when it's automated) is to revert the source to the last known stable commit after 15 minutes of the build failing. In other words, if you can't fix it, or don't know what caused the build or test to break, then revert it and work locally until it's resolved - never ever make other developers twiddle their thumbs while you grind away at a problem they don't care about.
P.S. If you already have a lot of tests failing, you can use a "trailing threshold" in CI. Set it up so that the build only fails if there are more test failures than last time. This, along with a coverage rule, will force developers to eventually improve the test situation if they want to be able to keep working.
P.P.S. I realize this might seem draconian to some, but it's all down your culture. If you get to a point where people just don't leave the build broken or tests failing (my team almost never does, although I occasionally have to remind them), then you don't need to continue with the strictest set of rules. Although IMO you should always fail the build on a broken unit test. Integration/browser tests can fail sometimes.