My favorite kinds of pastas are the hand-formed varieties. Don't get me wrong: My Atlas never leaves the kitchen counter, and we use it 2-3 times per week, but truly, truly...I love the hand formed stuff best.
Here are the types I'm currently making, or learning to make:
Orecchiette - get better at this all the time, as it's probably my favorite pasta.
Gnocchi - have it down with a fork, need a gnocchi board. :)
Strozzapreti - need work, definitely - just don't have that spiffy twist action down. lol.
Croxetti/Corzetti - I've faked this with some success; need to buy or build a croxetti stamp.
Garganelli - these are fun and easy. I like making them against my box grater, for texture.
Cavatelli - haven't made these yet, though I should. I am sort of waiting until I can get the Beebo cavatelli maker, so I can compare the "machine made" kind with the hand made kind.
Pici - I'll be honest, I've had varying levels of success with this and it looks *so darn easy*.
Farfalle - I finally killed my Atlas lasagna cutter making a huge batch of farfalle...this is one of those "in between" shapes for me - half-formed, half-machine. I still make it using a zigzag roller cutter for the edges...just takes a lot longer.
...and various forms of spaetzle, which are *kind of* a noodle, in my head. ;)
Pastas I can't get specifics on:
Trofiette - I can NOT find the flour/water ratios for this, nor can I find decent instructions on how it's made. I found a video on YouTube, but it bears no resemblance to what you buy dried. (lol - the video showed yet another pasta shape to make, though, though I have no idea what to call it.) If you have info, please let me know.
Frusciuddati - I've only HEARD of this one. Can't find a picture or information. It sounds like garganelli, but I'm not sure.
Since I find a new one every few weeks, I know I'm missing tons - what am I missing, here?
I'll save the filled pastas for another list. lol.
P.S. I'm English, Scotch, French, Czechoslovakian, Dutch, Bohemia, Russian, Irish, and American Indian - seems like there should be some Italian in there somewhere, but alas. lol.