These were really an exercise in imagination and there is nothing even slightly difficult or tricky about any of them.  These are all constructed from the bottom up and I will give you the patterns I used.  However, bear in mind that any stitch you like can be used, provided you pick up the appropriate multiple of stitches around the base once it has been completed.  Also, while the patterns explain how to do what I did, any method of creating a base (or ties, for that matter) will work just fine and you should feel free to go with whatever your favorite technique is :)

Size

All bags are roughly 4.5-5” in diameter and 4.5 - 6” in height.

Materials

About 50 grams, approximately 100 yards light, worsted weight cotton (original bags were made from Classic Elite’s Newport, discontinued, and Flash) Each bag takes about one ball.
Size 7 US (4.5 mm) needles (double points or circular - whatever you like to use to work in the round).
Size 6 US (4.0 mm) crochet hook

Bag - the 1st

Because I have a horrible time with casting on for something to be worked out from the center, I was looking for another way to handle things.  Hence the dishcloth base :)

Provisionally cast on 10 stitches.

Row 1:  Purl 10
Row 2:  Knit 9, turn (or wrap and turn on the short row - your preference)
Row 3:  Purl 9
Row 4:  Knit 8, turn
Row 5:  Purl 8
Row 6:  Knit 7, turn
Row 7:  Purl 7
Row 8:  Knit 6, turn
Row 9:  Purl 6
Row 10: Knit 5, turn
Row 11: Purl 5
Row 12: Knit 4, turn
Row 13: Purl 4
Row 14: Knit 3, turn
Row 15: Purl 3
Row 16: Knit 2, turn
Row 17: Purl 2
Row 18: Knit 1, turn
Row 19: Purl 1
Row 20: Knit 10, turn
Row 21: Purl 10

Repeat Rows 2-21 4 more times: 5 wedges total.
Release your provisional cast on and graft the cast-on end to the working end.  You can also do a three-needle bind-off if you prefer.  Run the yarn end around the hole it the center, draw tightly to close and fasten off on the back side.

Pick up 51 stitches around the edge of the base and mark the first stitch. 

Purl 2 rounds.
Knit next 9 rounds.
Do seed stitch for 5 rounds (*K1, P1*)
Knit the next 4 rounds.

Bobble round: K1, MB, *K2, MB*; repeat between *s around.  End K1.  (Make bobble thus:  K1, yo, k1 all in next stitch.  Turn.  P3.  Turn.  Lift second stitch over first and drop off the end of the needle.  Lift the third stitch over the first and drop it off too.  Knit remaining stitch through the back of the loop.  Bobble is complete.)

Knit 4 rounds.
Do 5 rounds seed stitch.
Knit 5 rounds.
Purl 2 rounds, decreasing 1 stitch on the last round - 50 stitches.

Next round:  K2, K2tog, yo, *K4, K2tog, yo*; repeat between *s.  End K2.
Knit 2 rounds.

Bind off loosely until you have one stitch left.  Do not cut yarn.

With your crochet hook, ch1. Sc in same space.
*Sl st in next st, ch3, sl st in first chain. Sc in next stitch.* Repeat around, joining with a sl st in first single crochet.  Cut yarn and weave in all ends.

Make a cord about 30” long (I-cord, monk’s cord, braid - whatever you prefer; the tie on the original bag is monk’s cord) and thread through the eyelets, knotting the ends so the cord stays put :)

Bag - the 2nd

Make a loop of yarn - no slip knot! - and work 8 sc into the loop (excellent tutotial here for Adjustable Ring).  Pull the end gently to draw the stitches into a circle (alternatively, ch2 and work 7 sc into first chain; join with slip stitch in last chain).

Round 1:  Ch 2, hdc into same space.  Work 2 hdc into each stitch around, join in starting chain.  16 hdc.
Round 2:  Ch 2, 2 hdc in next stitch.  *Work 1 hdc in next stitch and 2 hdcs in following stitch*.  Repeat between *s around, join in starting chain.  24 hdc.
Round 3:  Ch 2.  Hdc in next stitch.  Work 2 hdcs in following stitch.  *Work 1 hdc in each of next two stitches and 2 hdcs in following stitch*.  Repeat between *s around, join in starting chain.  32 hdc.
Round 4:  Ch 2.  Hdc in each of next 2 stitches.  Work 2 hdc in following stitch.  *Work 1 hdc in each of next
3 stitches and 2 hdc in following stitch.* Repeat between *s around, join in starting chain.  40 hdc.
Round 5:  Ch 2, hdc in each of next 3 stitches, 2 hdc in following stitch.  *Work hdc in each of next 4 stitches and 2 hdc in following stitch.* Repeat between *s around, join in starting chain.  48 hdc.
Round 6:  Ch 2.  Work one more round of hdcs, increasing 3 stitches evenly - do not join. (51 hdc)

Working into the strand just below the back loop of the stitch (see this post; scroll down for the crochet part and a general description of this technique), hdc in each stitch around and continue spiraling up (that is, just keep crocheting hdcs in the next stitch without joining) for about 2.5 - 3”.

Now you’ll return to working in regular rounds and to working the hdcs in the normal way by inserting the hook under both the front and back loops of the stitch.

*Hdc in each of the next 2 stitches, ch1, skip next stitch.* Repeat around, joining in first hdc, Eyelet row complete.

Ch 2.  Hdc in same space, ch1.  *2 hdc in next st, ch1.* Repeat around, join in starting chain.  Fasten off.

Go back to the base of your bag and cinch up the starting stitches with that yarn end so that there’s no hole.  Thread end through a tapestry needle, draw to inside of work and fasten off.

Weave in any other ends.  Make your tie (at least 30” long, longer if you prefer) in whatever fashion you like (the one on the original bag is braided).  Thread tie through eyelets and fasten ends together.

Bag - the 3rd

Begin as for Bag - the 2nd, with the same crocheted base except increasing to 50 stitches (rather than 51) on the final round.  Do not fasten off!

Switching to your needles, pick up the last crochet loop plus 59 stitches around the base - 60 stitches total.

Rows 1-6:  *Knit 5, Purl 5* around for 6 rounds.
Rows 6-12: *Purl 5, Knit 5* around for 6 rounds.

Repeat rows 1-12 once more and then rows 1-6 one more time.

Knit 2 rounds plain.

Next round:  *Knit 3, yo, ssk*, around.

Knit 2 rounds plain and bind off loosely.  Don’t cut yarn, but finish edge with a round of single crochet.  Fasten off and weave in ends.

Make cord (the cord on the original is I-cord) in whatever fashion strikes your fancy, and thread it through the eyelets.

Notes: Any of these little bags can be whipped up very quickly so they are a nice project if you don’t have lots of time.  They aren’t big enough to be used as general purses but with a little embellishment (or the use of some fancy yarn!) they could be suitable evening bags - big enough to hold money, keys and lipstick plus a little more :)