It really depends on who you fly for and if your company is a partner with a major. If your flying for a large regional you will most likely have recip jumpseat privileges on most airlines. You can also most likely nonrev on your company and the mainline partner.
Most regionals have jumpseat agreements with most airlines, so you can jumpseat where and whenever you want (within the agreements, i.e. maybe not international or limited seats for pilots from your company).
Now, if you are looking at travel benefits for your family that depends on whom you work for. At my company we have travel benefits on Delta, United (except those Houston based), and Continental (limited to those Houston based). Each partner is different, example: Delta; you, your wife, and kids can travel free in the USA and 3 international trips a year, but your parents pay a fee based on mileage. On United, they charge you and your family a fee based on mileage adjusted whether you sit in first class or coach. On Continental, I think (not Houston based) it is a flat 12.50 one-way for you and your family. There are also passes; you can purchase from other airlines as well though the travel department which can be a flat fee, ZED fare, ID90, etc. It can be quite complicated at times to figure how to get somewhere and how much will it cost you.
Cricket at Delta my parents have 18 travel days they can use for domestic travel..Int'l in different though...Employees also have certain travel days depending on time of hire until 10yrs and then unlimited...
We get unlimited free domestic flights on Delta and all ACA flights. We used to get United as well but they cut back and now the Delta side of the company only gets Delta bennies and the United side only gets UAL bennies (which, by now, are quite poor). Additionally, we get three free days of international travel on DAL.
My wife and kids get full benefits on Delta and ACA. My parents get free rides on ACA and ID95s (95% discount) on DAL.
I think that furloughees get benefits for something like 30-60 days.
As an AMR furloughee, we got non-rev travel for 90 days after our effective furlough date. We had to surrender our travel cards, and we were given a piece of paper (it kind of looked like a paper ticket) that was our authorization to travel. It was a pain in the rear to use! You had to go to the ticket counter at your origination city, wait in line, talk to an agent, convince them that you really did have authorization to fly as a D2, and then try to get them to give you your piece of paper back. The agents weren't trained in furloughee travel policies, so they would always try and keep that very important piece of paper, thinking it was a paper ticket that they needed to keep with their records!
AA had such a problem with people calling in sick who were about to be furloughed that for a while this summer anyone who was getting furloughed and didn't call in sick from the time they got their letter until their effective furlough date, they got 6 months travel privliges instead of the usual 90 days. I don't know how effective that carrot was in decreasing the number of sick calls.