I am designing a space and cost constrained layout. On it I have two analog muxes (ADG719 (datasheet) or similar.) Both switch states a maximum of two times a second. They do carry video signals with a bandwidth of around 10 MHz, but they aren't amplifying those signals, just passing them. So I figure I can omit the 100n capacitor which is normally installed next to all the ICs on my board. Am I okay in doing so?
You do need decoupling for all IC's that switch or carry analog BUT where the decoupling is located and how many there are is a matter of design. Noise happens and decoupling is essential to ensure that it does not 'happen too much" - but part of the designers role is to avoid blind and pointless use of excess decoupling. Placing a capacitor adjacent to each IC is traditional and safe enough but what matters is what is being achieved by the decoupling, not where the capacitors are located.
The object is three fold
The first two aims are complementary. At a board level, if you achieved either one wholly then you would not need to achieve the other. In practice they work together. Meeting the 3rd helps the other two.
In your case, if space is constrained then moving the capacitor somewhere else or using one capacitor in the place of two or more others is entirely acceptable provided that the object that was originally aimed at** is still met. ie this places more effort on you as a system designer to properly identify and quantify your noise sources, to properly understand the effect of noise on a given IC etc and to design a decoupling system that meets your needs.
Note that a 0.1 uF capacitor is almost certainly not the ideal size per IC - not so these days and possibly never so. Certainly 0.1 uF is often a fine compromise, but if you are trying to fine tune the result you may want a larger of smaller capacitor or possibly even several in parallel or several of different sizes in different locations. Also, as capacitor technology has improved things like ESR and lead inductance are smaller, surface mount packages give better electro mechanical environments (eg lead length minimal from an eg 0402 cap) and you may be able to use smaller or larger caps than in previous eras. Some suggest that a 1 uF ceramic cap is now a better general decoupling element than a 0.1 uF "monolithic ceramic" cap used to be, and others argue that a 0.01 uF cap is better able to handle the faster switching edges and clock speeds of modern systems.
For demanding situations it actually helps to look at specific data sheets and look at impedance/frequency curves. Capacitors of the same capacitance made with slightly different technologies (even amongst eg ceramics cap family) and/or from different manufacturers can and do have different enough frequency/impedance curves to be worth being aware of.
In the case of your multiplexers you should be able to estimate "within reason" the noise spikes originated by your ICs and the effect of system noise on them. Then by orientation of ICs, location of capacitors at sensible and critical locations etc you will be able to reduce capacitor count to under 1 capacitor for every IC.
Cost You say " ... and cost constrained..." on this point you are far less "safe". An ADG719 costs about $US1 in 10000s, falling to maybe $US0.80 in 100,000s. Maybe somewhat less in Asia. A decoupling capacitor costs around 1 cent for a 0.01uF or 0.1 uF in production volumes. Board space and mounting and inventory and ... costs more, but the IC also has additional costs. While every cent matters, a saving of perhaps 1% to 5% on a critical component should be a secondary issue. By all means eliminate the per IC capacitor if you can - but do not let cost be the deciding factor.
In response to query
What's acceptable deep-ends largely on what you are happy with.
If you have no other circuitry to react to noise spikes, or don't care about worst case outcomes, whatever they may be, then you may not care about generated spikes.
If noise from elsewhere does not occur, or is sure to be at a level where the effect on the video or IC is unimportant to you then you may not care about incoming noise. Extreme worst case response to noise may be IC "SCR" latchup or even destruction - but this would be "less likely" with low as opposed to no decoupling.
SCR latchup and death is a real world effect in some ICs. Less common in modern ones, by design.
The following references cover latchup in a range of devices. Only some of the following is specifically relevant but all may be of general educational value wrt the possible effect of out of range input transients on ICs.
You didn't supply a link to the datasheet, so we don't know particulars. However, any IC that contains digital signals at all should have a decoupling cap at first and even second approximation. The signals passing thru a anlog mux aren't the issue, it's the digital signals it uses to switch those signals and switch the FETs that will be passing or not passing the analog signals.
The frequency of switching has nothing to do with it since the problem occurs at the switching edges. If you ever switch at all, then there are probably short term current spikes. Each spike is a separate event and it doesn't matter whether the next spike is 20ns or 2 seconds away.
Besides, decoupling caps are small and usually not much burden on a layout. Surely there are other ways you can economize on space. You really really don't have room for a few 0402, or 0603 or even 0805 parts? I find that hard to believe. What about the bottom of the board?
To paraphrase Dirty Harry: Do you feel lucky, punk? Well, do you? Go ahead, leave off the decoupling caps. Make my day.
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If you really want to save cost, then add the capacitor now and leave it unpopulated if you are 100% sure that everything will be ok in every thinkable scenario. While it will still requires the boardspace, you might save the placement and part cost in the end.
Saving costs might be tempting, but in the end you risk having to do a redesign of the board together with a sample rerun. Also, completely verifying that the design will (always) work without the decoupling capacitor will cost a LOT of ressources and money, so maybe you should start saving at some other point in your design.
When deciding whether to use a coupling cap, I think the normal question should be whether anything in the circuit would be affected if, every time there is a change on an input which should cause something in the device to switch, the internal state of the device was randomized, and the state of all outputs would be randomized for a new nanoseconds. Note that analog inputs which are amplified count as "causing something to switch", but pass-gate analog connections generally don't. From a functional standpoint, I don't see wouldn't need for bypass caps in your device. On the other hand, if there is any noise on the supply rails from some other source, it could get capacitively-coupled onto your video signal. In such a case, if there's more noise on the VDD reaching the device than on its VSS, adding a bypass cap might help.