Despite the title, there is very little to be said about going faster than light.

Without ignoring all the important parts of the current understanding of physics, it is totally, completely, unavoidably impossible to travel faster than the speed of light

Frankly, the only example of actual FTL I know of is Starwar's Hyperdrive, which is never explained adequately so even saying that is pushing it.

pFTL
Pseudo-Faster-Than-Light, the real force behind almost 100% of effective space travel in fiction. pFTL is any system that subverts the speed of light to travel between two points in an amount of time less than that required by light, without actually traveling faster than light. There are numerous ways to achieve this, especially considering this is fiction and you're granted the ability to do whatever the hell you want.

I break it down to a few categories.

Warp
Surprisingly startrek has this almost exactly right, some years ago a physicist even proved it to be legitimately possible, if not even slightly feasible.

Expand the space behind you, shrink the space in front of you, creating a wave of space that you ride. The key is that the speed of light only applies to matter/energy, space to our knowledge is permitted to distort at whatever speed it pleases, and since it's the space you're in that's moving, you are effectively standing perfectly still.

Pros
Warping space is a relatively simple thing to do compared to the other methods, and if your drive fails, you've got no effective velocity so you just pop into normal space (unless you decide to make it work differently)

Cons
It's a very involved process, you have to constantly generate and sustain the wave form, expending amounts of energy every second that we're not capable of expending currently. More importantly, you don't leave real space, so it's completely possible, that is to say, more than likely, that you will collide with some piece of matter drifting through the universe. Now this is a tricky bit, you're not technically moving, so there shouldn't be anything meaningful in hitting something that's just mozying along, well that's where we bring in the fact that movement has to be measured against a frame of reference, a thing in the big picture that is for all intents and purposes not moving. So let's say that you are the frame of reference, well compared to you this chunk of junk is traveling at a speed exceeding the speed of light, which as you recall we can't go because it would take infinite energy to achieve the speed of light itself.

So this thing hits you at infinity+1 tons of force, and instantly both of you are smeared across the universe like a fine jam on whole wheat toast.

Dealing with that is not within the aims of this article.

Alternate Space
Invent an alternate space to travel in, have the rules be different, make the speed of light not the defining comparitive of mass, or much much higher

Pros
Unless you impose some sort of native affinity or buoyancy principal a failure of your drive will just leave you right where you are, which is good because an uncontrolled reentry has all sorts of bad implications, such as where you land. The speed of light works out to be the limit because that's the point where energy to increase a mass's velocity by 1 becomes impossible to calculate, not Pi impossible, divide by zero impossible, it simply doesn't function. What all that means is that if you raise C, it's conceivable that it will take less energy to achieve the same thing, so maybe you could pull of warp travel speeds with intrastellar energy sources

(note: Intra, inside, inter, between; intranet, internet)

Cons
If your drive dies, you're stuck, somewhere else, until you fix it.
If you don't fix it, you're screwed.
Alternative realities might contain things other than nothing, in fact it's likely they will contain lots of stuff, maybe even living stuff, or maybe there's just a constant ambient energy level equivalent to a black whole exploding, or all sorts of other bad things.

Jumping
First you're here, then you're there. It's really that simple. Keys to Jump travel are that A, it's instantaneous, and B, there is no intermediary step. You simply go from one point in space to another with no meaningful time between the start and the finish.

Pros
It's fast!
Since the travel is instantaneous the drive can only fail in a few ways, ether it doesn't work to begin with, you don't end up where you expected, or you arrive as a fine mist.

Cons
Unless you have the technology to see where you're going, you're traveling by guesstimation, probably aided by very powerful computers. You'll note Battle Star Gallactica uses jump travel, and they have to spend quite a while calculating how to get where they're going without killing themselves by landing, say, inside each other.

And Finally
Wormholes
Technically these are in themselves several different formats, you can have Farscape style wormholes that just kinda occur naturally, you can have stargate style wormholes that are generated on demand between specific points, you can have window wormholes that effectively take a circle of space here and a circle of space there and make it connect so you walk through, a lot like jump travel only not instantaneous, or just do whatever you want

Pros
It's hard to say, as a whole they offer a lot more functional problems, and a lot fewer fatal errors, but so much depends on how you do it that I can't really said. Just about the only clear advantage is that you don't need a wormhole drive to travel through a wormhole, somebody needs one but once the wormhole is there anything can travel through it, this makes them a great option for civil space-highways.

Cons
Wormholes are one of those flukes of special relativity, like time travel, they're not well understood and in all actuality man kind has never seen one, or anything to suggest one's presence. If you go with the natural sort then of course you're at the wormwhole's mercy as to when and where you are going. Generally speaking wormholes go both ways, so if you were to use one to send in your military, the enemy could take the moment to send a bomb through.

One thing to consider is that you don't have to use these by themselves. For instance, you may use a wormhole to get to the alternate universe with an exceptionally high C value, then use warp travel to push that even further.

Now you are of course welcome to ignore all the important parts of our current understanding of physics, but since you can do so much without expressly violating the universe as we know it, why would you?