Adding to 12Lappie's answer:
You can use 3x 74HC4051 for example (if the voltages you want to mux are compatible). So, each MUX has one analog output. Connect the MUX select inputs together, then to the micro.
Thus, you have 3 lines, which control all MUXes simultaneously (ie, if the value on these lines is 001, then the first input of each MUX is selected).
The decoder can be omitted. Simply direct the 3 MUX outputs to 3 analog inputs on your micro, and use this to select which MUX output you want to acquire. This uses 6 pins total.
Now... the filtering.
If all you want to do is amplify, you can share the amplifier between inputs, by putting it between the MUX and the micro, provided of course all inputs need the same amount of amplification. With this 3 MUX to 3 analog inputs scheme, you can use 3 amplifiers with different gains, if you want. Or you can use a single amplifier, but then you need to put the decoder back, as 12Lappie explained.
Now... the anti-alias filtering is another matter.
Remember, if you sample at (say) 1 ksps PER INPUT, then each input should have an antialias filter with decent cutoff at 0.5 ksps... and you cannot reuse it, of course. If you put the filter after the mux, and select each input in turn, then the output of the filter will be a jumbled mess of all inputs mashed together.
So, you need one filter per input. Not negotiable.
If your sensors are very high impedance (like, unable to drive the parasitic capacitance of your MUX and ADC), then you'll need the opamps anyway.
Otherwise, to keep costs down, the simplest solution is to use a dumb 1st-order RC filter, oversample like crazy, and apply the filtering in the digital domain, where instantiating 20 filters does not need 20x more parts, just a loop and some number-crunching. Simple IIR filters (ie, biquads) require little processing power provided your micro has a decent MUL instruction.
Now, the deciding factor will be the ADC sample rate, the sample rate you need to acquire after downsampling, and the highest frequency the analog signal can have that must be presevred. So, please provide this information.
Now... if your 20 sensors are measuring stuff like temperature... then why the hell aren't you using DS18B20 digital thermometers?