Big Thank You Mister E.
You and MELABs staff helped me to find mistake. I insert in my code two lines and now program works great. These are two lines:
DEFINE I2C_HOLD 1
DEFINE I2C_SLOW 1

Maybe, someone will have the same problems in future, so I decided to post all my code. It works flawless.
Thanks again
Vladimir

'PIC16f872
'---------------- Definitions---------------------------------------------
define OSC 20
'------------- Define LCD registers and bits------------------------------
DEFINE I2C_HOLD 1
define I2C_SLOW 1
Define LCD_DREG PORTB 'Set LCD data port
Define LCD_DBIT 0 'Set starting data bit
Define LCD_RSREG PORTB 'Set LCD register select port
Define LCD_RSBIT 4 'Set LCD register select bit
Define LCD_EREG PORTB 'Set LCD enable port
Define LCD_EBIT 5 'Set LCD enable bit
define DEBUG_REG PORTC 'Set DEBUD port
DEFINE DEBUG_BIT 1 'Set DEBUG pin
DEFINE DEBUG_BAUD 2400 'Set DEBUG baud rate
DEFINE DEBUG_MODE 0 'Set DEBUG mode



DPIN var PORTc.4 ' I2C data pin
CPIN var PORTc.3 ' I2C clock pin
bearing var word ' word size bearing value 0 - 359
bearing1 var byte ' byte size bearing value 0 - 255

Main:
i2cread dpin,cpin,%11000000,2,[bearing.Highbyte,bearing.lowbyte]

lcdout $fe, 1,"BEARING ",DEC BEARING/10

i2cread dpin,cpin,%11000000,1,[bearing1]

lcdout $fe, $c0,"Bearing ", dec bearing1

DEBUG " Compass Bearing ", # bearing,13,10

pause 20

goto main