I slightly disagree with the recommendation above to sign up for them all.

First of all, if you're interested mostly in international destinations on other continents, that limits you to the legacies.

Next, you need consider that some are dupilcates. For example, no need to sign up for both UA and CO and US. For that group, sing up for CO (because it's your CO-type number which will become your UA number once CO/UA finish merging), and use it for all CO, UA, and US flights.

Then, if you're interested in doing upgrades (with a combination of miles and cash co-pay), sign up for AA and sign up for DL. If, however, you're only interested in miles (for outright awards), sign up for AS instead, as it partners with both AA and AS. (That way you can have just two programs which cover all the US-based legacy airlines, and can redeem on all US-based legacy airlines.) But beware, you will not be able to upgrade (anything other than Alaska's own flights) if it's AS miles you collect.

And, btw, you need lots of miles in one program to get either free flights overseas or upgrades on paid flights. So if the price difference isn't too big and the schedule isn't too bad, I suggest you pick and first, second, and third priority on which program you'll collect in. (You won't be able to transfer the miles between programs if you wind up with them too scattered!)

And finally, you mentioned "lower the price". Sorry, there is no "cash + miles" option for award flights on any US-based airlines that I'm aware of. (BA is the only airline I'm aware of having such an option, at least in the past. They recently revamped their program, and so I don't know if even they still have that.)

And beware that using miles for those intenational flights will require that you be flexible. For example, it's very hard to use miles for free flights to many destinations on peak holiday dates any more.

Some are duplicates. For example, no need to sign up for both UA and CO and US, since you can sign up for one and credit flight on the others to that one. (UA and CO are merging, but at this instant are still separate as far as sign-ups go. Similarly, AirTran and Southwest are merging, but they are still basically operating independently as of this month.)

Furthmore, most have some sort of expiration-without-activity policy, so you'll have to keep track of that somehow, and learn techniques for keeping your miles / points in each alive if you have miles / points scattered across oodles of programs.

But some LCCs have expieration that you can't easily avoid! These I would suggest you avoid signing up for, and steer away from flying them, unless you're ready to do whatever it takes (possibly hold a particular credit card which may have an annual fee) just to keep the miles from expiring.

And LCCs will not get you to those international destinations.

And interni