On many flights, children younger than 2 can ride for free, but they have to spend the trip on their parents' lap. Saving money this way can be tempting, but in some cases paying for a seat might be worth the extra expense.
For one thing, in his own seat, your baby will get to ride strapped into a familiar car seat (as long as it's FAA-approved), which gives your arms a rest during long flights. Plus, you'll have the car seat available when you reach your destination. And the cost may not break the bank -- some airlines let young passengers ride for half price.
If you decide not to reserve a seat for your infant, try to travel during a time that's not busy. This makes it more likely there will be some empty seats where you can spread out. Some couples request window and aisle seats in a three-across configuration, so if nobody takes the middle seat, they can use it for the baby.