B757-200 EXPERIENCED SEVERAL GND CONFLICTS TAXIING INBOUND AFTER ATC ISSUED CLRNC TO THE GATE.

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AFTER LNDG ON RWY 27L AT ORD; WE EXITED ON THE HIGH SPD; AND CONTACTED GND ON 121.9 AS WE EXITED; WE WERE TOLD TO KEEP ROLLING TRANSITION TO TXWY B AND WERE CLRED ALL THE WAY TO THE GATE ON TXWY B. AS WE CLRED I SLOWED BECAUSE I NOTICED AN ACR Y B737 ON TXWY A SHORT OF TXWY R. AS WE APCHED TXWY R; THE ACR Y B737 TURNED INTO US AND ONTO TXWY B APPARENTLY WITHOUT CLRNC AND CUT US OFF CAUSING AN ABRUPT STOP ON OUR PART. WE SAID NOTHING AND CONTINUED TO THE GATE. AT ABOUT A5; WE WERE AGAIN CUT OFF IN A CLOSE AND DANGEROUS MANNER; THIS TIME BY ACR Z JET. AGAIN IN AN ATTEMPT TO GO WITH THE FLOW WE CONTINUED AND CONFIRMED AGAIN THAT WE WERE INDEED CLRED ON TXWY B; ALL THE WAY TO THE GATE; AND WERE REASSURED THAT WE WERE CLRED ALL THE WAY TO THE GATE. NOW AS WE APCHED TXWY A7 (I THINK) WE WERE AGAIN FACED WITH AN ACR Y JET THAT MADE A HARD L TURN OFF OF TXWY A ONTO TXWY B WITH NO APPARENT CLRNC AND NO INTENTION OF HOLDING SHORT OR GIVING WAY TO US. AS WE CONTINUED; NOW EVEN MORE ON GUARD THAN BEFORE; WE NOTICED AN ACR Y WDB ON TXWY A APCHING TXWY A10 (I THINK) THINKING THERE IS NO WAY THIS COULD HAPPEN AGAIN...WRONG; AS WE APCHED SAID INTXN THE ACR Y WDB SWUNG AROUND THE CORNER AT FULL SPD WITH NO INTENTION OR ABILITY TO EFFECTIVELY STOP; AND CONTINUED RIGHT THRU IN FRONT OF US. I FLASHED LNDG LIGHTS IN AN EFFORT TO SIGNAL TO HIM WITH NO LUCK. ON THIS LAST EVENT IT REQUIRED A SECOND HARD STOP (TO ANTI-SKID) TO KEEP FROM MAKING CONTACT WITH THE ACR Y JET. IN FACT; I WOULD SAY WE STOPPED ABOUT 10 FT SHORT OF THE ACR Y'S WING. NEXT STEP WAS TO HOLD EVERYTHING AND CALL GND FREQ ON THE CARPET. HIS RESPONSE; SOMETHING TO THE EFFECT OF 'YES YOU ARE CLRED ALL THE WAY TO THE GATE AND AS FAR AS ACR Y AND ALL OTHERS; IF YOU DON'T KEEP UP THE MOMENTUM THEY'RE GOING TO GO AHEAD OF YOU.' AT THAT POINT WE ASKED FOR A PHONE NUMBER AND CONTINUED TO THE GATE WITHOUT FURTHER ISSUE. I DID HEAR THE CTLR TELL SOMEONE THAT HE WAS NEW AT ORD. AT THE GATE AFTER THE CHKLIST; I SPOKE WITH TWR SUPVR WHO WAS NEARLY AS CAVALIER AS THE CTLR ASKING ME 'WHAT DO YOU WANT ME TO DO ABOUT IT.' THE TAPES SHOULD TELL THE STORY. THE SUPVR ALSO INDICATED THAT ORD IS A TRAINING TWR AND THAT THEY WOULD CALL ME BACK (WHICH THEY DID NOT). NEXT DAY AFTER GETTING NO RETURN PHONE CALL; I CALLED AGAIN TO BE HANDED TO HEAD OF TWR QUALITY ASSURANCE. I EXPLAINED THE SITUATION AND I ADVISED THAT I THOUGHT THE EXECUTION ON THEIR PART WAS EGREGIOUS AT BEST AND THAT THE ATTITUDE WAS BEYOND ANYTHING I COULD CONSIDER REASONABLE AND INTERESTED IN SAFETY. IN SUM: AFTER CLRING THE RWY WE HAD 4 HARD STOPS; 2 OF WHICH WERE TO ANTI-SKID TO AVOID HITTING OR BEING HIT BY XING TFC TO INCLUDE ACR Z; THE LAST OF WHICH (ACR Y WDB) I'M CERTAIN WAS ON OUR FREQ BECAUSE OF THE REMARK THEY MADE AFTER WE CALLED GND 121.9 ON THE CARPET UNION REP WAS NOTIFIED.