…or perhaps, more correctly, I know why they’re getting fried (static), but I’m curious why these things are so sensitive…
I have worked on ungrounded tables before, while standing on a wooden floor, handling all sorts of PCBs and PC cards, and never had a problem. I have destoyed 3 ICs in the last week, presumably due to static discharge. I’m going to ground the table - if I do this, do I need to wear a wrist or ankle strap as well?
What physically is happening within the IC?
-FK
Most ICs that are static sensitive are CMOS type ICs. The metal oxide insulating layers between components is VERY thin and easily punctured by static charges. Definitely do wear a wrist strap, your ICs will thank you for it.
It should be noted that often the damage done to a circuit board is not immediately obvious. It may work well until a certain instruction runs through it, or a certain buffer tries to dump its contents, or a certain XNOR gate tries to output a 1, etc. So the best bet is always to wear protection because you just never know.
If it’s a metal table, be sure to check for an actual current leakage.
Put a sensitive voltage meter between it and a ground wire to check. I’ve often seen extension cords with on/off switches, and power strips, fail by leaking a small current when “off” which can tranfer to the table.
Grounding the table may make things worse. What you need is a static mat which is connected to ground. The mat is conductive but has some impedence, so that when you do touch something the charge bleeds off slowly instead of one big dangerous zap. You will also need a wrist strap. Typically the mat and strap will ground through a 1 meg or so resistor, which is built into the connector (you don’t have to add your own resistor).
There’s another, much more important reason for the high impedance of antistatic grounding systems. If you’re working live on or with anything connected to line power, an accidental contact with the hot line is an instant electric chair if you’re connected to ground through a low-impedance connection.
Let me second what engineer_comp_geek said (and really, with a user name like that, how can we doubt him? 
):
Have a static mat with an integrated resistor in circuit to your wrist strap. The idea is not only to keep everything at the same potential, but also to limit how quickly the charge can transfer (ie, limit the current), when potentials aren’t equal. (Aside: even if you think the charge is equalized, moving equally charged materials closer and further away causes a change in capacitance that can cause temporary voltage spikes.)
Physically within the IC: A static discharge (even one you may not see or feel) is applying a transient voltage that can be in the thousands of volts, for a very brief time. If this current can’t be dumped to ground somehow, this causes pretty much one of 2 failure mechanisms: a dielectric breakdown between two conductors, or a line fusing open.
The dielectric breakdown is like a blown capacitor. There is a charge causing such a large electric field between two points on the chip that the insulator between the two is destroyed. This can be between 2 metal wires on the chip (either adjacent to each other in the same level, or vertically between two levels), or it can burst through what is known for a CMOS transistor as the “gate oxide”, which is the very thin dielectric that makes up the main part of a transistor, between the gate of a transistor and it’s source or drain.
A line fusing open is caused by a line carrying more current than it is equipped to handle - either because there is already a current path (perhaps the one mentioned above) blown, or because it’s normally a contact path between the two lines, or an ESD protection circuit. The heat from the (I*R) drop through the line doesn’t dissipate fast enough, and melts the line.
As circuits get more complex, all of these different wires get closer and closer together, which makes them more and more sensitive to static discharges. This is consistent with your comment that this is more common than it used to be - that’s well known through the industry.
Everyone tries to put some type of protection circuitry on the exposed pins of their chips. This circuitry does nothing in normal operation, but turns on a low resistance path when an extremely high voltage is applied. But again, these only have so much they can handle, and it gets harder and harder to design them as the chips get denser and the minimum sizes of the circuits get smaller.
Hope this helps - I’m always willing to go on with more detail than anyone wants on this topic.
Part of the problem may be that you’re frying IC chips when they are supposed to be lightly broiled for one hour after marinating in lemon juice and milk overnight.
You have had some very good advice so far (buy a static mat + wrist strap), but I’d like to address this issue:
Why has the failure rate spiked so drastically?
Has there been a change in weather? If the air is very dry, you will retain charge for longer, and buil d up higher voltages.
Have you changed clothes? [sub](I hope so)[/sub] Are you wearing more synthetic clothes now, than you were a couple of weeks ago? Certain materials (especially synthetics) help build up high voltages, when rubbing against your body.
What about shoes? You say that you stand on a wooden floor, which probably is non-conductive, but if it is humid enough, it might be enough to let your charge seep out - if your shoes are not too good insulators.
If this is a relatively new occurance I would check carefully the environment you are in. Are there any large motors or other sources of electromagnetism? They can also induce a current in a chip that will overwhelm it. Make sure also that you plug-in is grounded properly. An ungrounded plug is usually not a big problem but in a high static area you can build up quite a charge on the case of the computer or whatever it is you are dealing with.