—How many different ways are there to cast on? --
Depends on how you count!--if you measure by RESULTS there are fewer, if measure by TECHNIQUES, there are more, (and if measure by NAMES the list is almost endless!)
I KNOW (that is I can work them with out a reference book handy) about 40 cast ons. Inspite of my vast knowledge, my default cast on--(one used about 50% of the time!) is a LONG TAIL cast on.
I don't think I am alone in making this cast on my default—Because there are, dozens and dozens of ways to work this cast on—and even more names than methods. But if you compare the results—you'll find the different techniques all create the same result or nearly the same result.
If you have steadily refused to use Long Tail, maybe its because you haven't found the variation or construction that works for you!
First lets start with a definition:
Long Tail Cast on is a 2 yarn (usually) cast on that creates a set of simple loops, that are immediately worked as a stitch.
The long tail cast on has many names; most are references to how it worked.
An old name is 'Double' –because it is worked with 2 (double) yarns
Sling Shot is an other common name (the yarns held in the hand resemble a sling shot)
Thumb (the thumb of the left hand is used almost like a needle
Finger (the index finger is used almost like a needle)
Two needle (2 yarn) cast on—a long tail worked with a second needle (and not the thumb or index finger)
the Left hand cast on (a reverse of the sling shot method)
An Open Loop 2 yarn cast on
Sometimes a Long tail technique is worked with 2 balls of yarn –for extra long cast ons--(any time the cast on edge has 100 or more stitches) this guarantees the tail will never be too short—but 2 colors can be used for a decorative effect, too.
Then there are a series of variations of the long tail
--One variation is to double wrap the first half--(the thumb in sling shot and thumb) to have a double edge.
Twisting the thumb loops (aka Twisted, German Twisted, or Norwegian Twisted and other names) is a common variation—there are 3 or 4 methods for twisting the loop. Twisting the thumb loop by transferring the index finger is called a Maine Cast On.
Combining the Open Loop Long Tail alternately with a standard long tail gives the Estonian cast on.
Twisting the 2 strands of yarn between each cast on stitch gives a braid cast on –this is most commonly done with 2 different color strands, and can be done with multiple (up to 5) strands of yarn—or it can be done with a single color for a subtle attractive edge.
There is also a Double Row Long Tail –start with a loop or slip knot, *cast on 2, Pass first stitch over second, Repeat from *(be sure to leave a extra long tail—you'll need to cast on 2 times the desired number of stitches!)
There are (at least 3) cast ons that use 2 strands of yarn that are NOT members of the Long tail family—
the other is Judy's Magic cast on, (this is a close relation to the 2 strand tubular)
the third is the channel island cast on.
There are almost as many single yarn cast ons--
the Simple, the simple reversed, and alternately worked pairs of the each
the Knit, (also worked as a purl, and alternately worked pairs as a ribbed cast on)
the Cable (also worked as a purl, and alternately worked pairs as a ribbed cast on)
the Knotted—which has several names depending on how it is worked—I know 4 ways—and there could be more. (Russian, Gansey and Buttonhole are the three most common alternate names)
the Chain or Crochet cast on—This cast on also has several names depending on how it worked.
There are also several (I know at least 3!) versions of the tubular cast on worked with a single strand--usually after a Provisional cast on --
Provisional cast ons come in several forms, too—The main characteristic of all provisional is the ability to undo the cast on (easily) and leave live (open) stitches
There are specialty cast ons-the Turkish, and figure 8, the twice knit cast on, and noose, pinhole or eyelet cast ons—for starting work in the round—(3 different names for 2 basic techniques!—the Emily Ocker (a knotted cast on worked over a loop), and the disappearing loop cast on (a provisional style cast on worked over a loop) are styles of noose cast ons.
There are cast ons that are edging, too—the simple picot cast on comes to mind—it's made by casting on with a knit cast on, then binding off (2 to 5 stitches) and then continuing to cast on (X + the number to be bound off)--this cast on has a matching selvage stitch, and a matching bind off--
There is a second Picot Cast On, that is a knit version of a narrow hairpin lace—which is more commonly a crochet technique—A band of lace is worked, and then stitches are picked up from the looped edges of the picot (hairpin) lace band, the other edge is an open, decorative loop.
There are several lace edging that start with casting on, and immediately casting off, (the gaps in the cast on edge making lacey loops)--but these are often worked over several rows, making them an edging more than a cast on.
I-cord cast ons are another edge technique used as a cast on.
It is possible to knit for a life time, and to always use a single cast on technique—but many of the different cast ons have different characteristics—and knowing a few creates options.