I travel a lot. Less likely to take planes now, due to the new security rules., but still traveling a lot.
Sometimes I go get people from the airport or train station; sometimes people come pick me up. Sometimes neither. It’s nice when someone can be there, but no big deal if they can’t.
When I have friends/family coming into or returning to Montreal, I come and meet them at the airport if I can get away. It’s nice to see a familiar face, even beyond the practical reason that the airport is very disorienting.
Back when they were dating, my mom and dad had a fight and broke up, and she soon flew back to visit her parents in California. Playing music up in Mistassini, a Cree community in northern Quebec, my dad repented and wanted to call my mom, but didn’t have her number; so he waited in line at the band office, where the only telephone in the village was, and called his friend Dave in Montreal and got him to break into their apartment and find her date book with her parents’ numbers in it. He reached my mom and found out that she was coming back soon, so he came back to Montreal; but in his excitement he forgot to ask what date.
So, unable to call again for reasons unknown to me, every day for three days he went to (then-)Dorval Airport and waited and waited and waited as that flight number came in. On the third day she arrived, they made up, and they were together ever afterward.
I’m neither married nor dating anyone who travels, and the only member of my immediate family who does any traveling flies out of an airport that’s an hour away from me, but once a year my best friends and their little boy take a plane trip. I live much closer to the airport than they do, so we have this tradition where they swing past my house on their way, I jump in, and when they get out at the curb I drive their car back to my house --it stays in my parking lot for the week. When they come back home I take their car to go pick them up, and this time I go inside and meet them at baggage claim. Sure, I pay for the short-term parking, but I get to see them a little sooner and help them carry their stuff out to the car. And, there’s the additional benefit of having their son (who is currently 5) run up to me and give me a big hug when he sees me. 
I don’t remember the last time I had someone meet me at the airport, and I’m really not sure whether I’d want someone to or not. I guess it might be nice to have an SO meet me, but more for the knowledge that he missed me than for any practical reason. Actually, most of my flights are short weekend trips to NYC that don’t include any checked luggage, so I never see baggage claim – the closest anyone could get to my gate would probably be practically outside the airport, anyway. grin
My parents are retired with nothing but time, and yet they still didn’t offer to pick me up at the airport one hour away. They even were happy that I took the shuttle not just to the place 15 minutes away but switched shuttles to the one that took me five minutes away.
I would really have appreciated an airport pickup and I would do it for my friends anytime I could and it was appropriate.
Neither my wife nor I travel on business, so when we travel on vacation, it’s just us, and there’s no one to meet us.
From the other side of this, meeting people used to be a lot more enjoyable when they let visitors onto the concourses.
When I go to visit my parents, my mom always picks me up at the airport, and comes inside. I like the welcome and hug right there at security. It is only very recently that I’ve been able to convince her to just drop me off at the curb with my bags instead of parking and coming in while I check in (I’m 27!). In her defense, this is a long standing tradition in my family-- you go in and see them off at the gate. I was always nice to have company at the gate while waiting, and my mother liked to actually see the plane taxi out. But this was before 9/11. Parking at Newark is a HUGE hassle and even short term is now a serious hike with your luggage. I prefer the curb.
When coming home, my best friend often comes inside to meet me, and it’s very nice. Parking at SFO is not a problem, really, and neither of us travel very often. My other best friend travels more frequently, so he calls us when he lands, and we head out then.
Mrs. AG travels for work a lot (recently, on a weekly basis) and I always go to the airport with her (unless it’s in the middle of the work day). I’ll drop her off at the curb when she’s departing, but I’ll always park and wait for her right at the gate exit (and wait with her for her luggage) when she comes back home. Given that she flies Red Eyes quite a bit, some of her flights leave very late at night, and she always protests “I can take a shuttle”, but I always insist on driving her and am always glad that I do (and I think she feels the same way).
I’d love to be picked up or dropped off at the airport. My parents live about 5 miles from the airport but when I go visit I have to get a bus into the city and then another bus back out to their house which adds up to about 15 miles. It’s not really about the distance, just that it would be nice if they would sometimes think about whether it’s hard for me to cart luggage on buses and maybe offer.
When I fly home to visit my parents, the pickup situation depends on what time my flight gets in. If it’s mid-afternoon or so, then my mother will head to the airport when she sees online that I’ve landed, and I’ll wait outside the bag claim for her to come pick me up. If its late evening, my father will swing by the airport on his way home from work and, again, we meet at the curb.
However, if it gets in late (eg 8PM or later), both my parents will drive to the airport. One will avoid paying for parking by circling (because parking in Philadelphia is obscenely expensive), and the other will come in and make a big embarrassing scene in the bag claim area.
If given my choice, I’d just take a shuttle or public transportation home. Easier for everyone, probably just as fast and cheap, and better for the environment.