Air Carrier Captain reported two occasions of a critical ground conflict during taxi. The first was with an airline courtesy van that did not stop at the stop sign for taxiway/ vehicle crossing. The second; a baggage tug sped up to cross in front of the aircraft during taxi. Heavy braking was required to avoid an incident.

Narrative

While taxiing from [Gate] XX to Spot XX through the ramp; we were taxiing on the blue line behind company traffic on the orange line. We were given clearance to taxi from Ground Control to follow company on the orange line to XXL via Bravo Taxiway. Company traffic proceeded without incident and we followed. I was looking left to confirm vehicle traffic was stopped on the vehicle lane and I hear my FO (First Officer) say 'Hold it; hold it!' I looked right and saw a another airline's courtesy vehicle speeding through the traffic lane without any regard for the stop sign or the fact we were in constant motion past Spot XX. I stomped on the brakes to avoid a collision with the vehicle. The driver then noticed she had sped through the stop sign and sped up to avoid us. We were well past Spot XX and almost in the vehicle lane. I flashed my landing lights to bring the driver's attention to us. After we had stopped; other vehicle traffic apparently took the cue as a go-ahead to drive through the vehicle lane and we waited as several vehicles proceeded through. We reported the event to Ground Control. Once clear; I asked the FO to ensure none of the flight attendants were injured if they had been standing due to the sudden stop.This was the 2nd unacceptable ground vehicle incursion of the day. Earlier; a baggage cart sped across the ramp as we were taxiing; not allowing an acceptable distance between us and the vehicle. Instead of waiting; they sped up to avoid us as we were taxiing. I've been seeing an uptick in careless ground vehicle operation in the vicinity of the ramp space in and around the North satellite ramp area. Recommend reinforcement of ground vehicle operation and vigilance in and around taxiing aircraft on active taxiways to ensure right-of-way of aircraft.