Pros

• Any colour you like (even black). With some machines you can make rainbow stripes just like toothpaste tubes do
• Any consistency you like, and more or less eggs, or just egg yolks. Add baking soda or Kansui to make stronger, more shape-able pasta (not more than 0.5% or it tastes soapy in a sauce)
• Any flavour you like (herbs, spices, extracts, extra egg'y ...)
• Any flour you like (wholemeal and buckwheat is my favourite)
• Any shape you like, make lasagne sheets to fit your favourite lasagne pan, or make your own extruder dies (not trivial, but possible)
• Easier and quicker to cook
• Extruder machines give your arms a great work out
• Fun to do with children, and educational
• You control what ingredients go into it (more and more commercial pasta are including 'weird' ingredients for no reason I know of?)

The extruder you want :-)

Cons

• Expensive to make if you account for your time (you should)
• Flour is flour. The base tastes more or less the same
• Large amount of time to make decent pasta, especially in tricky shapes
• Pasta machines can be hard to clean
• Special hardware (roller, drying racks, extruder etc.) required for anything but the basic flat noodles

One of the best reasons to make fresh pasta is to make your own tortellini and ravioli. It is simply impossible with dried pasta, since dried pasta no longer sticks to itself. There are more variations of fillings than the standard "cheese" or "meat" that are otherwise unavailable if you only buy filled pasta at a grocery store.

There are some of us that do this as part of a slow food / living simply / homesteading type thing.

Some of the main reasons for doing this:

• Reduced packaging (eggs from the chooks, buy flour in bulk)
• Reduced food miles
• Focus on whole foods and reduced additives
• The enjoyment of producing something with your own hands and involving your family in production
• Ability to make things in larger quantities at a reduced or comparable price (I get my flour for free from a friend in exchange for the occasional pizza night)
• Ability to home-make things which can be shared for free or exchanged for free with neighbours
• Minimal or zero waste (flour bags can be re-used or composted), left over dough scraps and flour can be fed to livestock

With homemade pasta, you don't need any preservatives, and have complete control over what ingredients (quality, variety) are used. You can add elements for a specific flavor (spinach is common, beet is something I'd like to try, I could see basil, and now @lemontwist has me curious about squash...), or substitute ingredients for specific dietary or health reasons. I know several people who make their own pasta so they can make sure no salt is involved.

Fresh pasta is easier to cook, and doesn't require additional pantry space. You likely have all the ingredients on-hand.

Cheaper, customizable flavor (spinach, tomato, squash, etc), and in my opinion, far more delicious (ie fresh, different mouthfeel, and also because you control the ingredients you can use your favorite spices or veggies) than store bought. Only downside is the effort.

It's better for sure, it tastes great and you can choose better raw ingredients and quality flour. Moreover you can add veggies, spices, eggs and customize pasta in many ways. You can also choose the best shape that suits your condiments.