warning: this thread will bring out extremely strong responses with
1) 'I do everything safest way' camp appalled that someone would not bring a car seat on a plane. You will get safety statistics and doom and gloom from them.
2) the 'I'm overwhelmed with xxx kids and cannot physically carry a carseat' or 'my kids screams bloody murder in it' or 'another reason' camp that gives you the pragmatic reasons why they would *like* to do it, but can't for some reason and have accepted it.
both sides will flame each other. it will become a multiple page thread. there will be unkind words stated and even SHOUTED about it.
I recommend using the search function and reading through some threads... probably go back a few pages and you will find another thread if the search function isn't working.
do what you are comfortable with doing. Don't be bullied into not doing it or doing it because of others.
My experience? when I had one child, we brought it on board. It was a hassle and she wanted to sit 'like a big kid' (who was across the aisle). It was a hassle to carry even with the carseat carrying bags. When we wanted to take it out, it was difficult to fit into the overhead compartment.
We now travel with 3 children (5,4,2 last time) ... and between sippies, snacks, coloring books, toys, Daddy's laptop, my camera, changes of clothes for all of us (I was thrown up on a flight once by a kid - VERY thankful for the extra clothes I had brought), diapers, wipes, etc. I just physically can't do it. I've learned my limits and a car seat is not within them. Plus, my kids end up switching seats halfway through the flight, which wouldn't work it a car seat was there.
Figure out what you are comfortable doing...
btw, I personally *hate* the rental carseats... maybe I had a bad experience, but the two times I've done it, they've been installed incorrectly and were very uncomfortable for the kids (one was the big bar that came over her head and she kept sliding around in it). For safety and comfort's sake, I will always check my own car seats and boosters... that is my concession to safety...