For example, in a shopping cart, I may buy this purchase for myself ("me" / "myself" icon), as opposed to gifting it to someone else (box with bow-tie icon). What is the ideal icon to represent ME?
Steam, a digital download games shop, shows both options on the cart view. The options are "Purchase for myself" and "Purchase as a gift" as buttons. I prefer this over checkboxes in this case as it has a deeper meaning in Steam as you can choose the recipients user account so the game gets added to them directly.
When it comes to a "me" icon not even Facebook has one (they use a text "Profile" link instead), but I think a generic silhouette would work as that's what you're used to represent yourself until you upload a picture on any site.
Since this is about shopping (i.e. money is involved), I would probably spell it out rather than having two different icons. Maybe an icon in a button with the texts "myself" and "gift" would work.
You may just want to consider using text labels instead of icons. Very few icons are universally known - most require a second or two of parsing. Using tags in a smaller lighter text next to product descriptions might be the most practical solution to your quandary.
However, if you absolutely need to use an icon, you could do something clever like take a generic head icon and insert either the recipients initials in it, or just say Mine! in text underneath.
The most intuitive icon of 'me' would be a picture (or an avatar selected by them to represent themselves) of the person. So for example if your sign in was associated with Facebook, you could use their profile picture.
I'm guessing this isn't a practical response though, so I would agree with other responders to say that you're probably better off as leaving it blank/generic (yet distinctive from other images) as a default option and use text as appropriate. For most sites and most shopping behaviours the default of not needing/wanting gift options will be appropriate.