I am trying to interface a microcontroller (MSP430) with another chip through I2C. Both datasheets (MSP430 and the other chip) advice me to pull the I2C signals up to VCC. Do I need to pull SDA & SCL signals up twice, for the microcontroller and for the chip, or not. Also each one of the chips specifies the values for pull up resistors, one says 10K and the other one says 5.1K. If the case is to pull up one time, which value I'll use?
No you don't. Use only one pullup. The value of the resistor is not that critical. Use something in the range of 5k to 10k. That will be fine.