I purchased a game for a gift and I forgot to click that it was gift. Is there a way once it's purchased to send it as a gift?

You should contact support and explain the situation, they may be able to help. :)

http://www.gog.com/support/contact

I have almost a week ago and have had no response. So I thought I would ask here.

Just make certain that you do NOT download it yourself. Once you do that, it's considered yours and is then not gift-able unless you buy another copy to gift.

That I made sure of, I haven't. As soon as I realized what I did I emailed support.

Did you get a confirmation mail that Support received your request and opened a support ticket? Unfortunately, the Support team is the only one who can help you with your problem, but I can confirm that they are very helpful and will turn your purchase into a gift code, provided you haven't downloaded the game yet and you can tell them your order number. If they didn't react yet, I'd suggest you try again; maybe your request got lost somehow. They usually reply within 1-3 days (weekends excluded)-

A week is long for them, but they might have some holidays too.
Sure they will get around to it, else just send them another ticket.

A week is a long time for support. I'll give one of the Blues a holler, see if they can see to the matter.

I did receive a response that a ticket was opened, It was purchased under my wife's account. I will have her open another ticket. Thank you all for the help.