
The TI ADS1298R could be perfect for that EKG project you dreamed of. It has a 8 analog to digital converters with programmable gain amplifiers, an internal reference, and a clock source.
The ADS1294/6/8/4R/6R/8R incorporate all of the features that are commonly required in medical electrocardiogram (ECG) and electroencephalogram (EEG) applications.
FEATURES
- Eight Low-Noise PGAs and Eight High-Resolution ADCs (ADS1298, ADS1298R)
- Data Rate: 250SPS to 32kSPS
- Programmable Gain: 1, 2, 3, 4, 6, 8, or 12
- Unipolar or Bipolar Supplies: AVDD = 2.7V to 5.25V, DVDD = 1.65V to 3.6V
- Built-In Right Leg Drive Amplifier, Lead-Off Detection, WCT, PACE Detection, Test Signals
- Integrated Respiration Impedance Measurement (ADS1294R/6R/8R only)
- SPI™-Compatible Serial Interface
- TQFP-64
This is a massive analog chip. Thanks McZ!

Well… This part costs around $48 USD each in unit quantity. With a little looking, it can be found (DigiKey has them). It comes in a hard to use for prototyping 64-LFBGA package or a more friendly 64-TQFP form.
There is a TI demo board for this part, P/N ADS1298ECGFE-PDK, $246.46 USD each at DigiKey.
Another approach would be to use individual I2C addressable A/D’s on a shared bus. Less pins, less cost(?), certainly more flexible IMO – use more or less channels, more or less resolution – up to you, not the part.