Strike-anywhere matches: They aren't what they used to be. Companies are saving money by putting just the tiniest heads on them.
Lifeboat matches: Burn furiously, but they take some practice to use and they're pricey. They'll break if you try to strike them like regular matches. Try jabbing them downward at just a bit of an angle, almost like you're trying to poke them through the striker.
Bic and/or Cricket butane lighters: Usually reliable, cheap and light. No excuse not to have a couple in your pockets.
Sparklite: Excellent piece of gear. Very small and light, can be used with one hand. As with the above butane lighters, there's no excuse not to have a couple of these scattered about in your pockets and packs.
Blastmatch: Another excellent piece of gear that can be used with one hand. There's magnesium in the large synthetic flint, and it throws a good shower of sparks. A bit bulky in your pocket, but definitely worth having.
Swedish Firesteel: Works well with two hands. But do your good knife a favor and use a bit of hacksaw blade - or even better, a broken Sawzall blade - as a striker. The larger "Army" model appeals to me more than the smaller "Scout".
Magnesium blocks with a synthetic flint glued on: Cheap ones, like those from Coghlans, tend to fall apart when you need them most. Milspec ones are commonly available and are more reliable, but they aren't easy to use. It takes several minutes of work to accumulate a pile of shavings, which have a frustrating habit of blowing away in the slightest breeze. Still, they're light and unaffected by moisture, so I usually have one available.
Magnifying glass: Useful not just for starting fires, but also to help identify mushrooms, remove slivers, etc. It's obvious weakness as a firestarter is that the sun must be shining, so it won't help you when you need it most. I once saw an antique tinder box with a "burning glass" built into the top. I thought making one would be a fun project, but I still haven't gotten around to it.
Fresnel lens: These are thin sheets of plastic that work like a magnifying glass. They're so small, light and inexpensive that it's worth owning several. They'll crease if you don't pack them properly, but will still work. I use them as bookmarks - I rarely travel anywhere without reading material.
Wind-resistant lighters: Several companies make "storm proof" or "wind proof" butane lighters. I bought a "Helios" from Brunton for a pretty penny. It worked well for a few weeks, but then it quit when I really needed it, on a long backcountry trip. I sent it to Brunton for repair. It again worked for a few weeks, and was sent back a second time, then a third, then a fourth. Adding to the frustration, Brunton's technical support people were terrible about responding to emails requesting return authorization numbers. It was an unimpressive piece of gear backed by unimpressive service. Perhaps other brands are better. I've noticed that the online reviews of Windmill brand lighters are more positive than those for Brunton's, and I'll probably try one if I stumble across a good sale.
With all of the above, take them out and use them before you need them. Have fun practicing in your back yard when it's windy and raining. It's too late to learn to swim when the boat is sinking.
Tinder is almost as important as the actual firestarters, and I haven't found anything better then cotton balls soaked with petroleum jelly. Just put a few cotton (make sure they're real cotton) balls in a heavy-duty plastic bag with some petroleum jelly and squish them around. When you need to start a fire, pull one out and fluff it up a bit. Hit it with a spark and it'll burn furiously for a couple minutes. Fringe benefit: The petroleum jelly feels good on the cracked hands and lips you invariably have on camping trips.
