There is monetary value, usefulness, thoughtfulness and emotional attachment.

The monetary value is the obvious element and has the most direct link to the overall value. If my wife asks for a specific birthday present that costs thousands of dollars, it has a high monetary value, it's probably useful, there has been zero thought put into by myself and it's all rather emotionally detached. (Other than the fact that satisfying my wife's desires is my reason for living of course.) Conversely if my young daughter spends all her money on a cheap screwdriver set that will last a month after Father's Day, it has low monetary value, it's pretty useless but she the fact really thought about it means it has a very high emotional value to me; and I'd probably cherish it for years (but never use it).

Usefulness isn't just about practical things like tools, car accessories etc.. Ugly jewelry isn't very useful, but a beautiful necklace is. Gift cards are the most useful but are viewed by the majority as being a "cop out". This is probably a bit unfair if you're trying to buy a gift for a distant uncle you know nothing about. A good idea when giving a gift card is to suggest something to buy with it. Perhaps something you like at that store or something you'd like to try. The recipient can take that into account and (probably) buy what they want, but at least you have demonstrated that you have put some thought into it.

Thoughtfulness is actually a subset of the emotional attachment but is an important element that the receiver and onlookers use to evaluate a gift. No matter how much thought you've put into it, if they don't think you have, then it will be a disappointment to them in some way. Spending lots of money on something can offset this, but it is still perceived that you have treated it as a chore. When giving a gift try to explain why you chose that particular thing. Sometimes, of course, they just don't like it, but that shouldn't be viewed as a failure.

The best gift is one that makes a person really happy. This can be done in the ways described above, but to get that special thing can really resonate. You really need to know the person, whether it's a spouse, partner, child or parent and ACTUALLY put a lot of thought into it. Whether it's a specially painted picture of your car by your daughter or that signed Hank Aaron baseball you never, ever thought you would get, you really feel you have got the best present ever and that really does make the giver happy too.

So, is it the thought that counts? Yes, of course it is, if you have actually thought about it and demonstrate that to the recipient.