Amniocentesis and chorionic villus sampling (CVS) are genetic tests that can be used earlier to find out the sex of your baby. They are more invasive and can pose health risks to your baby. Though these test also yield better information about genetics. Many mothers are fearful of using the tests solely for finding out the sex and wrangle with whether they even want to know anything about genetics. This can make it even harder to figure out. The risks of these tests are inherent to the test and have nothing to do with genetics. So your baby may not have any genetics issues and may still miscarry from the test and vice versa.
Some families are choosing to use alternate means to try to figure out the sex before birth. This might be one of the store bought tests like the Intelligender Test. This is not regulated by physicians or midwives, you can buy it online or at local stores. It's supposedly valid from the 10th week of gestation. And there are also the old wives tales.
There is also a new method of finding out the sex that is gaining in popularity, it's called the Ramzi's Method or Ramzi's Readings. This uses ultrasound in early pregnancy, as early as six weeks pregnant, to be able to tell the gender of your baby based on the location of the placenta. Most physicians don't offer this per se, but you can certainly ask about it.
There are newer tests on the horizon that are not yet ready for the general public. Most are looking at the baby's cells being shed into mom's blood stream or urine. The hopes are that these tests can quickly and accurately tell newly expectant parents whether their baby is a boy or a girl. While some advocates will claim that this will help with bonding during pregnancy, others worry that gender disappointment may set some mothers and fathers up for depression in pregnancy. There are even those who worry that knowing early on will increase the abortion rate if a parent finds out in the first trimester that they are having one sex over the other.
While many Americans don't think about it, finding out the sex of your baby has been banned in other countries. This is largely for fear of sex selection purposes.
At the moment, we are probably within a decade of these earlier tests. They may not be readily available once they are fine tuned, however, do to patents and protocols. This would make them available only to those who could afford them or had insurance coverage for the tests. (Insurance may or may not cover them, it is speculation at this point.)
Until these tests are available we have the technology that is discussed above and many fun games and folklore designed to help us enjoy the art of guessing the sex of our babies.