This is my understanding:
1) The blood and urine tests are to double check levels of things like progesterone (low levels could indicate problem and potentially lead to miscarriage), and they check protein the urine, which rules out kidney issues, I believe. I would do those, as they are relatively inexpensive and can catch a variety of issues that are easily treatable but can do serious damage unchecked. They also test for STDs because some can be passed on to the baby and may require immediate treatment.
2) 1 hour glucose - this is a test for gestational diabetes I believe. When you are pregnant, your blood absorbs sugar more quickly, which means your pancreas (I think?? maybe another organ) may not be able to produce insulin fast enough, causing gestational diabetes. Even if you eat healthy, anything you buy prepackaged or from a restaurant has added sugar, as does any drink besides water usually, so you may be eating more than you think. I would personally be hesitant to skip this unless you were on all organic, whole foods, nothing prepackaged diet. Gestational diabetes can be terrible untreated.
3) Anatomy scan at 20 weeks is good, they can tell a TON about the health of the baby, and if everything looks good, you shouldn't NEED another. I did have one more to confirm the baby's position since my baby was sideways til right before I delivered.
4) If you don't want to screenings on the baby for things like Down Syndrome, those can be easily skipped.
Now, lot's of people go without any of this stuff and do just fine. Some don't. If you trust your doc, then discuss the tests with them, what you can learn, and why should do them. My personal minimum for peace of mind is the blood tests, the glucose tests, and the 20 week anatomy scan. Then regular check ups where they examine you and check the heartbeat.