Is it legal for a parent to give a loan to his child.

That's what parents are for.

It's very tough for kids whose parents cannot/will not help out financially.

I've always been happy to help out whenever requested.

It's very rewarding.

Much better than letting it rot in the bank.

Seconded

- also, try not to attach 'strings'
- generosity is fine, but using it as a lever is unpleasant

Make sure you have paperwork drawn up so that it is a loan and not a
gift.  Giving over a certain amount will cause tax and estate
consequences in the U.S.

Yes, have a written loan agreement including an interest rate that is
acceptable to the IRS as not being so low that it considers the loan
as a hidden gift.
If there are other children in the family, this is, of course, the
only fair way to handle it.  Having a payment schedule for at least
the interest makes the loan more "official", and also makes sure the
"child" understands that it is a loan.
When the loan has been settled, s/he might be urged to start saving
the amount of the payments, having learned to get along without the
amount.

As Nelson mentioned:  final settlement of the loan can be netted
against inheritance from the same person, but I hope that is a long
way off.

The legality is the easy part.  I'll suggest that the potential
hardships on your relationship are much more important.

Loaning money to a friend or relative has ruined countless
relationships.  If your child fails to pay you back, they will still
be your child and you cannot allow this to put any strain on that
fact.  Your child will always feel awkward around you if they can't
pay you back.  The relationship will not be the same.

I only loan money to friends/family if I'm willing to consider it a
gift or loan.  I let them know that upfront too; "If for whatever
reason you can't pay me back on time or ever, then consider this a
gift and I don't want it to affect our relationship"

If this is not acceptable then perhaps you could go a slightly
different route and cosign a loan for them.  This has its own
positives and negatives, but I think the potential to ruin a
relationship is less than with a direct loan.