What pasta sauces can I make that don't include cheese? I've been making a fairly standard arrabbiata sauce for months, and I'd like to expand the number of sauces I can make.

However, many of these recipes involve cheese and/or milk, but I'm sadly lactose intolerant and would prefer to avoid these ingredients.

What others sauces could I be making, and what pasta should I use with them?
Tomato Sauce
Putanesca
Pesto (omit parmesan)
Bolognese (meat sauce)
Squash Puree (maybe with sage)
Olive oil infusions (fresh herb/garlic/chilis/lemon zest)
Roasted Red Pepper puree sauce
etc