(And as of 12/12/12, this color represents an even later update for iPhone5.)
Of course, you can pay your U.S.-based carrier prices and just use your phone in Israel. But those prices are outrageous. There is a cheaper way - go local. Get a local Israeli phone number and pay significantly cheaper local rates.
My proposed solution works only if you own a GSM-based iPhone 4. In other words, Verizon iPhone 4 users can stop reading right now. Update: but many sites report that Verizon has issued their new iPhone 5 (which has a GSM slot) with the GSM unlocked. Thus, for world travelers the Verizon iPhone 5 may be the easiest and most cost-effective solution. However, some online news sites suggest that Verizon may switch the unlocked state off in some future iOS software update (this happened before with other carriers) - so be warned! In the meantime, Verizon has announced it will unlock the SIM on the 4S upon request.
What you need to do is unlock your phone from your current carrier to turn it into an unlocked (sometimes: "universal") iPhone 4. All this means is that your device (which has a unique identifier) is no longer locked into your U.S. carrier's system, and can be universally used with any GSM-based network in the world. Then, when you get to Israel, purchase a Pay-As-You-Go (PAYG) microSIM GSM card with minutes (and even PAYG 3G data schemes are available).
Turn your phone off. Pop out your U.S. carrier microSIM card and put in the Israeli card. Turn your phone back on. You now are on a native domestic network, with your own Israeli number. If you set things up correctly, you can even have English language prompts when connecting with network services. I have experience with the Israeli phone carrier Orange, but there are other carriers such as Cellcom. The Orange PAYG card is marketed as "big talk" (all lower case; here is the link to the Hebrew page.).
Update: the iPhone 5 uses a new GSM SIM card format dubbed the nanoSIM. Israeli carrier Cellcom is reportedly selling the nanoSIM already (for 99 NIS) as Israelis have already started showing up at Ben Gurion airport with brand new unlocked iPhone 5s. I do not know yet if the other major carrier Orange Israel makes its PAYG chip in the nanoSIM format. Remember, the iPhone 5 is not yet officially available to the Israeli market. There is already information that a cutting tool exists for turning a microSIM into a nanoSIM, and while there is a slight reduction in the thickness of the nanoSIM card, users report that the slightly thicker cut-down microSIM will work in an iPhone 5. But be warned!
So the key for this simple solution is to possess an unlocked iPhone 4. You have 3 options for getting an unlocked iPhone:
1. Buy an unlocked iPhone
Apple has been selling unlocked iPhone 4 and 4s devices since late 2010. They are very expensive, insofar as they are sold without the carrier subsidy that comes with a contract. Prices as of today start at $649 for a 4s 16GB (an 8GB 4 goes for $549). Update: Similar prices for an unlocked iPhone 5: $649 for the 16GB; $749 for the 32 GB; and $849 for the 64GB.
There is also a grey-market on eBay, but the savings of $50 or so might not be worth the trouble.
(Or, if you are willing to take a step in the direction of an Android-based phone, Google has started selling their "lead" device, the Galaxy Nexus, for $349 unlocked. But that is a different matter completely.)
If you already own an iPhone 4 or 4s, there remain 2 options:
2. Have your off-contract iPhone 4 unlocked by your U.S. carrier
If you are lucky enough to have an AT&T iPhone 4 which is currently beyond the initial 2-year contact (congrats! you own the phone and have paid the same high price for your device, only you've spread out the extra $400 over 24 months, and paid a little extra to boot), you can request that AT&T unlock your phone. They will do so. This program began in early April, 2012. Check here for the procedure. Update: if you are buying an iPhone 5 and are already the owner of an iPhone 4, AT&T will permit an unlock of your older iPhone 4. After AT&T sends you the acknowledgement, all it takes is a backup and restore via iTunes of your current iPhone 4. Make sure you do this before you activate your new iPhone 5.
3. Do it yourself
If you can't go either of these routes (you own an iPhone 4 or 4s still under contract), there remains a number of software "hacks" (aka "jailbreak") which can turn your device into an unlocked state. If you aren't tech savvy, this third route might prove to be too daunting. But it can be done.
(12/12/12 Update: there is another way for the AT&T iPhone5 - find a service that will unlock your phone through adjusting your locked status on the Apple database. Search for the term "IMEI Unlock" - and make sure you use a reliable, authenticated service like Applenberry - but be warned: these are not free.)
Be warned! These are software solutions, and can be wiped out if you refresh or upgrade your phone to some newer iOS version number. There is a small tug-of-war going on between Apple and the hackers who creatively come up with these solutions. If you have version envy, and feel you must always upgrade your phone to the latest and greatest, you have to resist that temptation. Sometimes, Apple will release an upgrade of the iOS for the sole purpose of "closing" an opening in the system architecture utilized by the hackers. Also, as part of maintaining control over their product, Apple says that you void the warranty if you do any of these alterations. You'll have to decide if it is worth the tradeoff of the Apple or carrier warranty that comes in exchange for this increased functionality. Millions of iPhone users (but still only a small percentage) have performed these various software alterations successfully. But if your phone goes haywire at some point in the future, you might well be out of luck with Apple.
The methods are different depending on whether you have an iPhone 4 or 4s, and what version of iOS you are currently running. You may find your version number under Settings --> General --> About --> Version.
I can't cover every variation - 4 or 4s, and the numerous iOS versions (and then there is one more issue: the baseband version of your phone). I can recommend that if you've gotten this far, take a look at my prior post, which gets into the technicalities, but is a little outdated. It isn't hard to find reliable information for your phone model or iOS/baseband combo. And there will be circumstances where you are simply out-of-luck: there are certain circumstances (let's say you just bought a new iPhone 4s under U.S.-contract with the latest iOS pre-installed) where the hackers haven't yet caught up to the latest Apple software release.
Update: Me? I just upgraded my iPhone 4 to iOS 6.0 with the official AT&T/Apple unlock. No more jailbreaking for me (at least not for unlocking). My subsidized iPhone 5