I tried to make a digital clock.

$0 = (7 + 1 + 2) \times 0$  
$1 = (2 + 7 + 1) ^ 0$  
$2 = (7 + 1) \times 0 + 2$  
$3 = 7 \times 0 + 2 + 1$  
$4 = 2 \times 7 - 10$  
$5 = 7 - 2 + 1 \times 0$    
$6 = 7 - 1 + 2 \times 0$  
$7 = 7 + 1 * 2 \times 0$  
$8 = 7 + 1 + 0 \times 2$    
$9 = 7 + 2 + 1 \times 0$  
$10 = 1 + 2 + 7 + 0$  
$11 = 12 - 7^0$  
$12 = 12 + 7 \times 0$  
$13 = 12 + 7 ^ 0$  
$14 = 7 \times 2 + 1 \times 0$  
$15 = 7 \times 2 + 1 + 0$  
$16 = (7 + 1) \times 2 + 0$  
$17 = (7 + 1) \times 2 + 0!$  
$18 = (7 + 2) \times (1 + 0!)$  
$19 = 10 + 2 + 7$  
$20 = 17 + 2 + 0!$  
$21 = 7 \times (2 + 1 + 0)$  
$22 = 7 \times (2 + 1) + 0!$  
$23 = 17 + (2 + 0!)!$  or $(7-2-1)! - 0!$  thanks to stack reader  
$24 = 2 \times 7 + 10$  

[Edit]  
What the hell...lets do it for minutes also (I cheated a bit):  

$25 = (7 - 1 - 0!)^2$  
$26 = 27 - 1 + 0$  
$27 = 27 + 1 \times 0$  
$28 = 27 + 1 + 0$    
$29 = 27 + 1 + 0!$  
$30 = 10 \times \lfloor\frac{7}{2}\rfloor$  
$31 = \lceil\log(17!) \times 2\rceil + 0!$  // $\log(17!) = 14.5510$  
$32 = (1+0!)^{(7-2)}$  
$33 = 17 \times 2 - 0!$  
$34 = 17 \times 2 + 0$  
$35 = 17 \times 2 + 0!$  
$36 = \frac{70}{2} + 1$  
$37 = \lfloor\ln {7}^{20}\rfloor - 1$ // $\ln {7}^{20} = (38.9182)$    
$38 = \lfloor\ln {7}^{20}\rfloor \times 1$ // $\ln {7}^{20} = (38.9182)$  
$39 = \lfloor\ln {7}^{20}\rfloor + 1$ // $\ln {7}^{20} = (38.9182)$  
$40 = 10 \times \lceil\frac{7}{2}\rceil$  
$41 = \lceil\ln {7}^{21}\rceil + 0 $ // $\ln {7}^{21} = (40.8641)$    
$42 = \lfloor\ln {72}^{10}\rfloor$ // $\ln {72}^{10} = (42.76666)$  
$43 = \lceil\ln {72}^{10}\rceil$ // $\ln {72}^{10} = (42.76666)$    
$44 = \lceil{(\ln 710})^{2}\rceil$ // $({\ln 710})^{2} = (43.1027)$      
$45 = \lfloor\log(10!) * 7 - \ln(2)\rfloor $  // $\log(10!) = 6.5597$  
$46 = \lceil\log(10!) * 7 - \ln(2)\rceil $  // $\log(10!) = 6.5597$  
$47 = 7^2 - 1 - 0!$  
$48 = 7^2 - 1 + 0$  
$49 = 7^2 + 1 \times 0$  
$50 = 7^2 + 1 + 0$  
$51 = 7^2 + 1 + 0!$  
$52 = \lceil\log(2^{170})\rceil$ // $\log(2^{170}) = (51.1750)$  
$53 = \lfloor\ln(17!)\rfloor + 20$ // $\ln(17!) = 33.5050$  
$54 = 27 \times (1 + 0!)$  
$55 = \lceil\ln(27!)\rceil - 10$ // $\ln(27!) = 64.5575$  
$56 = \lfloor\ln(17^{20})\rfloor $  // $\ln(17^{20}) = 56.6642 $  
$57 = \lceil\ln(17^{20})\rceil $  // $\ln(17^{20}) = 56.6642 $    
$58 = 70 - 12 $  
$59 = 7^2 + 10$