I would like to try to make fresh pasta. However, I do not have equipment like rolling pins and pasta machines. Is there any pasta shape which I can make without this equipment?
There are dozens of types of fresh pasta that are made without any special equipment. Many are not difficult at all, but might take some practice. Some examples include gnocchi, pici, orecchiette, cavatelli, farfalle, garganelli...there are many others. Some use a textured board to create ridges, this can be approximated with an unused (new) hair comb, other use "tools" you probably have at your home (such as a dowel or chopstick). There are many videos on You Tube that can help you understand the shaping technique, just search by the name of the pasta. Here is a good one for starters, though it also includes types of pasta that you would need a roller to make. You might also pick up some tips from this terrific project called Pasta Grannies.
Thanks to the answer by moscafj, some comments, and my own research, I am making a list of pasta shapes which do not involve difficult techniques and which can be made using minimal equipment (butter knife, fork, rod or chopstick).
Butter knife / Fork
Rod / Chopstick