I officially have a new obsession! For the last few months, I have been making my own donuts for my family and they are amazing! None of us will really eat store bought donuts anymore now! Lol. These are the two recipes I tend to stick with. I will post a separate entry for the glazes I use.

Quick Donuts:
2 Packets Fast Rising Yeast
1 Cup lukewarm water
3 TBLS sugar
1 egg, well beaten
1/2 tsp cinnamon
1/3 Cup melted butter
1 tsp vanilla
1 tsp salt
3-4 cups AP Flour
oil for cooking (I use veggie oil, about an inch in my big pot I use to cook pasta)

In the bowl of your mixer with the dough hook attached, add yeast, water and sugar. Allow mixture to sit until bubbles form on top of mixture (about 8 minutes depending on the temperature and humidity of your kitchen).
Add the rest of ingredients and mix with dough hook, knead dough for 1 minute. (Add flour about 1/8cup at a time until dough is no longer sticky, amount needed depends on the humidity of your kitchen, I usually use about 4 cups).
On a floured surface, kneed by hand for an additional minute. Roll out to about 1/4″ thick and cut out donuts. You can use almost anything to cut them out, use either a large biscuit cutter for the outer circle and a smaller one for the hole, or a large glass for outer circle and a shot glass for the hole, anything really. Rekneed the scraps together to cut out more donuts, but no more than three times or the dough becomes too tough and does not rise properly.  This recipe will yield about 20 donuts and 26 donut holes (the 6 additional ones will come from the last of the scrap dough).
Place donuts and holes on a lightly floured surface and cover with a slightly damp kitchen towel (with the space this many donuts takes up, you will be tempted to use a single bath towel, do not, it will be too heavy for the donuts to rise properly). Allow to rise for 30-45 minutes. (I usually wait the half hour then set up the oil pot and begin to make the glazes for the last 15 minutes).
Place the donuts in the oil, no more than three at a time. Fry for 1-2 minutes per side then flip. The donuts will be golden brown. Transfer to a large plate covered in paper towels or napkins to drain. Drop in glaze while still warm.
The holes will only take about 30 seconds each.
Any left overs can be frozen before they are glazed for another time. Freeze for up to 6 months, although they never last that long around here.

Bread Machine Donuts:
1/2 cup milk (80*F)
1/4 cup water (room temp)
1/4 cup veggie oil
1 egg, room temp, lightly beaten
1 tsp salt
1/4 cup sugar
3 cups bread flour
1 packet active dry yeast

Add all ingredients to the bowl of your bread maker. Use the dough setting and turn it on. Check after about five minutes, if dough is too sticky, add flour 3 TBLS at a time until it is not sticky. Allow bread machine to do its thing. Rise should take about an hour to an hour and 20 minutes depending on your machine.
When dough cycle is over, turn risen dough out onto a floured surface and roll out to 1/4″ thick. Cut donuts as before, this should yield 2 dozen depending on size.
Place cut dough on a floured surface and cover with a very slightly damp kitchen towel. Allow to rise until dough does not bounce back when pressed slightly, about 45 minutes.
Fry as before.