Is two hours before flight time early enough to show up at the Tel Aviv airport for a mid-morning, El Al flight to the States on a typical Wednesday? Or are the lines there so long that three hours is advised.
The lines at Ben Gurion Airport are short, some of the shortest in the world for an airport of this size (there's a reason for this—long lines are bad for security). Check-in lines can take about 40 minutes tops (less if your flight leaves soon), and passport control usually takes no more than 5 minutes (maybe 15 at peak times, but I have never seen more than this). The standard onboard bag screening line takes about 10–15 minutes too.
The problem, as
chx also said, is security: if you are deemed 'suspicious', prepare for questioning, which could take ~2 hours. They are usually nice about it if your flight departs soon, and might rush you through certain stages after ascertaining that you are safe. However, this is a good reason to follow the semi-official recommendation and arrive at least three hours early.
Judging from my recent personal experience (November 2016,) I would definitely advise getting there the recommended 3 hours in advance, especially if you're traveling by yourself. This was also the advice I received consistently from locals while in Israel a few weeks ago.
More Detailed Answer
Your actual wait times will depend on how many other flights are leaving soon on an airline whose check-in desks are in the same area as yours. Arriving much more than 3 hours early, however, is not helpful because they will not let you go through the line for the exit security interview that you have to do before checking in:
The security check is open for every passenger who arrives up to three and a half hours before the flight. The airline check-in counters are opened three hours before the flight's departure time. Passengers are required to present a valid passport and the flight ticket or a proof of purchase of a ticket (electronic ticket).
Source: Website of Ben Gurion Airport (and also observed in personal experience)
The process at Ben Gurion is a bit different from most other countries in that there is an extra step at the beginning:
The first step is a security interview that you must go through before you can check in for your flight. The interview itself wasn't particularly long when I went through it. They just asked standard questions to make sure that you didn't seem like a terrorist and that there weren't holes in your story and such. However, if they feel like it, they could start opening up and searching through your luggage which will obviously take a lot longer. This includes your checked luggage, which you will still have at this point and which must be marked by the interviewer before you can check it in with the airline.
Which line you go through for this interview depends on which airline you're departing on, with several airlines sharing the same interview line. This can result in the line length being highly dependent on how many of those other airlines are operating departures near yours. They do, however, go through the queue and give priority to people with departures coming up soon.
The second step is actually checking in with the airline. At least in the case of an Alitalia flight to FCO, I was not allowed to check in online in advance, but instead had to go to the check-in desk. Fortunately, this was relatively quick for me because my SkyTeam status allowed me to use the priority check-in lane, but otherwise it would have taken a while.
The third step is showing your boarding pass and passport at the entrance to the security line.
The fourth step is going through the security line. If you're unlucky like me (likely because I'm a young adult who was, at this point, traveling alone,) this means going through a 'special' line where they open up your carry-on and swab down every last thing in it, as well as requiring you to take off your shoes, belt, etc. All electronics had to be separated out (not just laptops, but all electronics.) Fortunately, though, at least I didn't get the strip search treatment to which chx was subjected. This part of the process took a while, as they could only process 2-3 people at a time and it took a few minutes per person.
After going through security and re-assembling all of your carry-on and clothing items, the next step was exit immigration. This was pretty straight-forward with nationals of most countries (basically any country with biometric passports) being allowed to use automated kiosks. Unfortunately, the facial recognition software doesn't seem to be all that great and it didn't recognize me, resulting in another few minutes delay waiting for an immigration officer to manually override it.
Once you've cleared immigration, you can finally go to your gate.
Also, before even getting to the airport terminal itself, there are security checkpoints on the road entering the airport. These didn't add more than a couple of minutes delay in my couple of experiences, though.
Time Required in My Experience
In my case, I arrived at Ben Gurion about 6 hours before my flight, as I was traveling to the airport with the rest of my tour group, which was leaving on a different flight (they were going to Newark on United; I was going to Rome on Alitalia.) Both United and Alitalia used check-in desks behind the 'A' security interview queue, but I wasn't allowed to enter the queue there until 3 hours prior to my flight's departure. Fortunately, they do at least let you wait in a relatively comfortable food court area until you can enter the queue. Around 9:00 AM on a Thursday, the A interview queue was relatively empty. However, by the time I was allowed to enter the queue around noon, it was quite long with several flights checking in on different airlines. From the time I entered the queue until I had completed the interview was a bit over an hour.
After going through the interview, it was around another hour for the remainder of the check-in, security, and immigration process (even with priority check-in.) By the time I finally arrived at the gate area, it was only about 50 minutes prior to departure (i.e. about 15 minutes prior to the stated boarding time.) Had I entered the security interview queue 2 hours prior to departure instead of 3, it's likely that I'd have missed my flight and this is without going through the more intensive search procedures that chx experienced.
In total, this was a time of over 2 hours from when I entered the queue for the pre-check-in security check to when I was actually in the boarding gate area.
The information in some answers above is outdated. On my last trip from Tel Aviv airport I waited full, nasty 60 minutes for passport control, and it's as terrible as it sounds. I would never plan to arrive to Tel Aviv airport less than 3 full hours before the scheduled departure. Arriving 2 hours before flight is very edgy, you will probably make it, but you can also miss your flight. Less than 2 hours - you are in trouble. And this is my advice for Israelis. For foreigners - I wouldn't dare arriving less than 3 hours before departure.
Two hours? Absolutely not. If the security people are not happy with you for whatever reason, they will escort you politely to a little booth where you will be asked to remove (almost) all your clothing, sit there in your underwear as they screen those and then they will remove every. single. piece. from your luggages and hand inspect it. I have went through this at the Eilat airport and Ben Gurion too. On the same day. I missed both of my flights, needless to say. (And I have been let back into Israel some years later -- haven't tried flying from an Israel airport since this happened, though.)
The waiting time in TLV is surprisingly short and procedures are fast. That being said - if you are of any "suspicious" Characteristics - you will need more time.
Two hours should be enough.
Interestingly enough, The last time I have visited there, I showed up three hours before, but the check-in (and security) for my flight was only two hours before the flight - so I was facing an empty counter with no security personnel. When they finally arrived, they cleared the area and started the process.
If you indeed are being held for further questioning - this can take more time, but the security people will most of the time do everything they can to rush you to your flight in time. I have noticed that the listed boarding times in TLV are many times not accurate (earlier - on purpose) and that the real boarding and departure times are late - and I think it is for this exact reason.
If you have anything suspicious in the bag (electrical items, tools etc.) allow more time, and be honest about it from the start! One time they took my bag out of the cargo area when I was already sitting inside the plane - and brought it to me to identify. This caused 30 min delay in the flight.
Be aware though, that like any other country (and even more) the TLV airport is affected by specific days / periods / holidays of extreme traffic. For example the Jewish Passover week, or the period following the Jewish new years holidays are considered peak periods in which it is best to arrive 3 or even 4 hours ahead.