In a No-Limit Texas Hold'em game of poker, a "standard" bet is
generally considered to be 3-5x the big blind. How, if at all, does
this change once antes are involved? Since the standard bet is meant
to manipulate the pot odds of a call, I would think the antes must be
accounted for in some way.

A "standard raise" is usually 3-5 X the big blind.

When antes are involved, of course the pot odds are changed, but the
perception of the raise has not.  The antes will continue to rise as
do the blinds so the relationship between the two will be similiar. 
When there is a raise, the purpose of the raise is to announce that
you have a hand and (or give the perception you have a hand.

Some poker books, such as Dan Harrington's series, account for the
antes, because then the initial pot becomes large enough to warrant
"stealing" the blinds and antes.

Big Blind $10
Small Blind $5
Ante $1 (times about 8 people)

That is a total of $23 in the pot vs $15 that would normally be in the
pot.  In my experience, that warrants a 50% larger raise since the pot
is 50% larger.