I consider BASIC the primary reason why I'm a sysadmin now, instead of a programmer. The problem I had with BASIC is that after years of tinkering with it as a kid [TI 99/4A, C64, GWBASIC on PC], I had a horrible time learning to get away from the 'GOTO' way of thinking.
In high school, I took the "Computer Math" class, which was basically learning how to do algebra in BASIC. I took that class because I had experience with BASIC at home, and thought it would help bring me to the next level. It was only years later that I realized that I should have taken the "Computer Science" class, which taught Pascal.
As a result of only being exposed to BASIC, when I tried to learn other languages or do anything more complicated than drawing circles randomly around the screen, I could never get the hang of functions and pointers and passing variables or whatever. So I decided I was too dumb to be a programmer, and wasted all my time playing games instead. I think if I had taken the Pascal class early on, I'd have had a much better foundation on which to build.
In the years since, I've become somewhat proficient with bash scripting (with functions and everything) as a sysadmin. I can sorta-kinda read some perl if it's not too obfuscated. I keep trying to learn Python, but I don't do it often enough for it to stick in my head.
While I have no desire to push my daughter to be a programmer [or do anything computer-centric] I do expect to ensure that she's at least exposed to some sort of programming, so that she has at least a reasonable idea of what makes all her computers and gadgets actually work. I have no desire for BASIC to be the thing that I use for showing her programming. Perhaps LOGO [how can you beat moving a turtle around for a kid?], and maybe Python.
I like the idea of python because, much like BASIC back in the day, you can very easily start a command line interface, and get action immediately.
BASIC:
10 print"Hello"
RUN
Python
>>> print "Hello"
Quick and simple, but without the danger of getting stuck in the rut of GOTOs.