MY BASIC, 29 bytes; BBC BASIC 27 bytes

for i=0 to 0xa*0xa
print i
next

Try it online!

Edit: Thanks for upvoting! I have found there is a BASIC dialect with even shorter syntax for hexadecimals (it's in BBC BASIC):

for i=0 to &a*&a
print i
next

that's minus 2 bytes :)

BBC BASIC, 29 19 bytes

I have revisited my first answer that I have posted more than 3 years ago and found out that the bytecount could be significantly reduced:

• -4 bytes thanks to @Neil for the comment he left more than 3 years ago! (Substituting 7 bytes PRINT i with 3 bytes P.i. Note that the alias P. is majuscule.)
• then again, -4 bytes by doing the analogous replacement of FOR i (5 bytes) with F.i (3 bytes) and NEXT with N.
• -2 bytes: removal of two spaces

F.i=0TO&A*&A
P.i
N.

MY-BASIC, 32 bytes

for i=0 to 0xa*0xa
print i;
next

Try it online!

Edit: Thanks for upvoting! This has been my original golf but it has turned out that BBC BASIC has an even shorter syntax for hexadecimals as well as handy for golfing aliases :)

MY Basic, 29 bytes

for i=0 to 0xa*0xa
print i
next

Try it online!

MY BASIC, 29 bytes; BBC BASIC 27 bytes

for i=0 to 0xa*0xa
print i
next

Try it online!

Edit: Thanks for upvoting! I have found there is a BASIC dialect with even shorter syntax for hexadecimals (it's in BBC BASIC):

for i=0 to &a*&a
print i
next

that's minus 2 bytes :)

MY Basic, 29 bytes

for i=0 to 0xa*0xa
print i
next

MY Basic, 29 bytes

for i=0 to 0xa*0xa
print i
next

Try it online!