Here's an easy pattern for holiday gifts!
I used "Countrywool's Easy Mitten Pattern" by Claudia at Countrywool and a pair of mittens from the cover of a mail order catalog as the basis for my striped version.  These go quickly; I made a pair in one evening!  Worsted weight yarn is ideal for these mittens.  I used my favorite Lamb's Pride Worsted (available at many yarn stores or click on the 'Countrywool' link above--no affiliation, but great service & yarn, plus Claudia is a regular & valuable Knitlist resource!)

MATERIALS:
Brown Sheep Lamb's Pride Worsted yarn (85% wool/15% mohair, 4 oz skein has 190 yds)  1 skein each 2 colors of your choice (I used Blue Boy #79 and Sun Yellow #13).  You can easily get 2 pairs of mittens from the 2 skeins of yarn.
double point needles US #4 & #6 (I also used a 12" circular needle size #6 for the main part of the mitten).
2 ring markers and a small stitch holder for the thumb gusset.

GAUGE:
4 1/2 sts=1" on #6 needles.

SIZE:
My pair will fit an average size adult hand comfortably (I like my mittens to be a bit roomy).  Claudia says to subtract 6 stitches for a child's size & to add 6 stitches for a huge adult hand.

Stripe Pattern:  Work 4 rounds in Color #1, 4 rounds in Color #2, repeat.

Cuff:
With #4 needles and Color #1 (Blue Boy in my pair), cast on 32 stitches.  Join and work in knit 1, purl 1 ribbing in the round, placing a stitch marker at beg of round.  Work in stripes (switching colors every 5th round) until cuff measures 3" or desired length--my mittens have 3 blue stripes and 2 yellow stripes, and ended after the 4th round of the blue stripe.

Next round: Continue working in stripe pattern as established!! Switch to #6 needles; *knit 8, make 1 st*, repeat around: 36 stitches (I "make one" by picking up the bar between stitches and knitting into the back of it.  Makes a nice nearly invisible increase).

Next round: Knit 1, place 2nd marker, knit around.

Thumb Gusset:
Round 1: slip 1st marker, make 1 stitch, knit 1, make 1 stitch, slip 2nd marker, knit around (38 stitches).
Round 2: knit around.
Repeat rounds 1 and 2 until there are 13 stitches between the 2 markers/48 stitches total (your 2nd increase round will be: slip 1st marker, make 1 stitch, knit 3 stitches, make 1 stitch, slip 2nd marker; 3rd inc round will be: slip 1st marker, make 1 stitch, knit 5 stitches, make 1 stitch, slip 2nd marker, etc).

Hand:
Knit across 13 gusset stitches, then slip them onto a stitch holder or piece of waste yarn.  Continue knitting around on remaining stitches, increase 1 stitch at end of round, placing 'beginning of the round' marker after the increased stitch: 36 stitches.  Continue working in the round and in stripe pattern as established for another 2 1/2" (my mitten has 2 more yellow stripes & 2 more blue stripes above the thumb gusset), then work in color #2 (yellow) only for remainder of mitten.  Work until mitten is long enough to clear your little finger (4" above the thumb gusset in my case).

Top Decrease:
Round 1: *knit 4, knit 2 together*; repeat around: 30 sts.
Round 2: knit
Round 3: *knit 3, knit 2 together*; repeat round: 24 sts.
Round 4: knit
Round 5: *knit 2, knit 2 together*; repeat around: 18 sts.
Round 6: knit
Round 7: *knit 1, knit 2 together*; repeat around: 12 sts.
Round 8: knit
Round 9: *knit 2 together*; repeat around: 6 sts (Note: I like to use a #4 needle for the last decrease round, as it helps alleviate those large 'loops' when you pull the final 6 sts. together).
Cut yarn, leaving a 12" tail; with a darning needle, run the yarn through the remaining 6 stitches and pull tight.  Weave in end.

Thumb:
Worked with Color 2 (yellow).  Pick up all stitches on thumb holder, using #6 needles, arranging the stitches around the needles & picking up 3 stitches across the 'bridge' where you cast on the stitch when starting the hand--16 stitches.  Join work, placing marker if desired to note beginning of round.

Round 1: knit around (I like to knit into the back of those 3 picked up stitches on the 1st round to tighten them up and avoid a hole).  Continue knitting around until thumb measures 2 3/4" or desired length (should clear the top of your thumb nail).  Next round: *knit 2 together*, repeat around--8 stitches remaining.  Close as for top of mitten.  Weave in all ends.