Playing techniques
General
Playing cymbals with drum sticks did not start before around 1900 when the drum set began to evolve as a new concept. Before that, drum sticks were to play (snare) drums. Cymbals used to be played hand held and in pairs, in the way symphonic musicians and marching bands still perform. Today's set drummers, however, sometimes don't seem to know, that there is more than just hitting cymbals with the tip or bow of a drum stick.
As you know from your own musical experience, there is a lot more of sonic possibilities in cymbals than just banging away on a half-open hi-hat and a couple of crashes (just in case of a butt end type rock/pop drummer... Never mind.)
All to obvious, the sound of a cymbal is influenced by what you use to treat it, and how you use it. Even if you don't subscribe to some of the more esoteric techniques mentioned below, there is a wealth of sounds possible with just regular drum sticks.
Quite often, a drummer falls in love with a cymbal played by another, only to be disappointed when playing it him/herself. This may be due to two facts: First, cymbals may sound quite different with varying distance of the listener. Second, even if said drummer would eliminate the first cause, s/he might still not be able to achieve the same sound as the other drummer. S/he could be using the same stick, mimick the playing technique, and still no avail? Well, the drummer's touch is another important factor. Playing soft or hard sure makes a difference, but that's not all there is. The cymbal, the stick, and the arm (body, actually) of the drummer compose a resonant system. All of them work together in producing the sound. Apart from the aspect of timing, two drummers will just not sound the same, due to their different weight and physical flexibility, their different resonance.
Striking tools
Here is a selection of more or less common drum sticks:

1 2 3 4 5 6 7 8
Left to right:
- Rutes. A bundle of very thin sticks tied together with a plastic band. Gives the ping of a very small stick together with the mass of a big one. Lets you ride even on crash cymbals. The weight brings ou the body in the cymbal's sound, while the ping remains tiny and sharply defined. Nice 'phasing' effect due to the mini sticks all sounding different.
- Hopf 7AN, oak, nylon tip removed. A very defined stick for ride playing because of the small contact area and the hardness of the wood.
- Vic Firth Arnold F. Strong taper makes this one fast. Ticky ride sound.
- Sonor 10A Maple. A large stick but still usable because it's quite light. Big olive bead causes a big ping with lots of high end spread (in other words, less defined)
- Vic Firth SD6 (tip end). Small ball bead gives a dry stick attack. The weight brings out the body in the cymbal's sound.
- Vic Firth SD6 (felt butt end). Handy to have on a drum stick for soft washing rolls.
- Schlagwerk rubber ball beater. A bit harder than the felt above. Good for bell type thick cymbals with a high resonance.
- Felt mallet with bamboo handle. Big, soft, light. For very soft swelling washes.
Riding
Playing a cymbal continuously, preferably with the tip of the drumstick. Jazz drummers often use thin ride cymbals (and no specific crashes), so they can crash and ride on one and the same instrument, maintaining a steady ride beat with interjecting shoulder crashes (crashing the bow, rather than the edge, with the tapered part of the stick). A dry cymbal with relatively quick decay of high frequencies is needed here, because a long sustaining cymbal would drown the ride attacks in its ongoing wash.
Crashing
Striking the bow with the shoulder of the drum stick. Crash/Ride depicts the habit of accompanying with crash strokes and also the type of cymbal made for this (mostly found in loud music styles like rock).
Choking
Stopping the cymbal's vibration right after a crash attack resulting in a 'choked' sound. Mostly used with splash and crash cymbals. In the 20's and 30's splashes were preferably used in this manner.
Rubbing
By rubbing a cymbals surface with the butt end of a drum stick in circles around the cup, howling overtones may be brought out. Quite a bit of pressure is needed so that does not work on small cymbals. If you never tried this, some practice will also be required.
Rolling with soft mallets
By rolling on a cymbal with tympani or yarn mallets, beautiful swelling (crescendo) effects may be achieved. Mostly used in soft/slow passages of ballads and other 'moody' music. This is also a common technique in symphonic music.
Bending
Thin cymbals may be bended (carefully) with one arm while striking them with the other. Thus the tension in the cymbal is varied, and with it, the pitch. May be applied to thin hi-hat top cymbals as well by varying the pressure on the foot pedal. Beautiful pitch-bend effects may come out. The effect is more sublime, so a calm environment with ample dynamic space is required (soft passage in drum solo, for example).
Bowing
Thin cymbals may be treated with a violin bow at the edge. This brings out sustained airy, flageolet-like overtone mixes. In case you never tried this, do so!
Other possibilities
If you're already bored by all this you might try one of the following:
- Try scratching a lathed cymbal (one with ridges and grooves) with a coin in a quick motion from bell to edge.
- Use a heavy knitting needle to play instead of a drum stick.
- Strike a cymbal in such a way that only the highest overtones emanate, then move the palms of your hands up down around the cup. Don't touch the cymbal and mute it, though. A good working distance is from as close as you can get without touching to a couple of inches. Nice phasing effect!
- Mount a not to small, not to big thick cymbal on a stand and give it a good spin, then strike. Whirly!
- Use a screwdriver with a metal shaft and strike the edge of a cymbal so that they meet in a 90 degree angle. Lots of silvery overtones...
- Use a heavy gong or bass drum beater to work on a large cymbal's edge. The larger the better.
- Elaborate on your own experiments and let me know about the results!