Python 2, 66 Bytes

Technically this causes an error after FF, but it does reach 30.

n=1;a='0123456789ABCDEF'
while 1:print a[n/16]*(n>15)+a[n%16];n+=1

I assumed string formatting wasn't allowed since I'm pretty sure it would go through base conversion, but if it was allowed, this would be 29 bytes:

n=1
while 1:print"%x"%n;n+=1

Python 2, 66 55 Bytes

This should really have been the most obvious approach to me..

a='0123456789ABCDEF'
for x in a:
 for y in a:print x+y

Old (66 Bytes): Technically this causes an error after FF, but it does reach 30.

n=1;a='0123456789ABCDEF'
while 1:print a[n/16]*(n>15)+a[n%16];n+=1

I assumed string formatting wasn't allowed since I'm pretty sure it would go through base conversion, but if it was allowed, this would be 29 bytes:

n=1
while 1:print"%x"%n;n+=1