I'm actually surprised noone came up with this yet.
Make the two planet's orbital planes about adjacent, and add a bit of ellipticity to them:
Pros:
* The planets barely meet each other - their orbital period can be made about the same, without the risk of collision.
* Even when they're close, their relative speed is extremely high: they are moving adjacent.
* Traveling between the two planet always needs very high delta-V, so it's technically very challenging, and has a really high energy cost. A slingshot maneuver is probably required, which takes a lot of time – years.
* Story-telling-wise, it's really easy to explain: it's a much simpler concept that the Lagrangian orbits.
Cons:
* The system is somewhat unstable - except some special cases - as comments pointed out. While you didn't specify if you want one, this may be a problem if you do want a hard-science answer - otherwise you could just hand-wave it, possibly blaming some other planets' (unexplained) stabilizing effect.
* Astronomically, it's really unlikely a locally born planet would earn such an off-plane orbit without a serious event.
So, how on Earth (khm) could a planet end up with such an orbit? I see three options:
1. It's an alien planet: it came from the outer space billions of years ago, and got caught. It's more ancient than any other planet there - sounds like a cool plot point, with huge possibilities. ;)
Note: This needs some other, possibly gas-giant-sized planets in your system to interact with.
2. 801
The solar system experienced a cataclysmic event in the distant past: experienced an orbital system breakdown, got "hit" by a fast-moving black hole, encountered another solar system, etc., that highly disrupted the planetar orbits. This must've caused collisions and an extreme bombardment as well – so fill your system with asteroids and craters ;)
3. Even better - the planet got caught from the other star system causing the cataclysm above! This has all the advantage of (1) and sounds better and more feasible than (2), actually. (I'd imagine it's a bit hard to earn a 90° orbital plane shift from zero... but if the planet always had it... ) Maybe it's life was already developed at that time? An advanced civilization was destroyed in the cataclysm?... story points, story points everywhere... 801