A nice place to start in thinking about this question is book I of Aristotle's Nicomachean Ethics http://classics.mit.edu/Aristotle/nicomachaen.1.i.html
There Aristotle addresses the nature of happiness and consider the pros and cons of three sorts of lives: the life devoted to pleasure, the life devoted to money, and the 'political' life (or the life devoted to honor). You don't say in your question what you have in mind by 'glory,' but it seems similar to what Aristotle had in mind by honor, namely, others bestowing on us recognition or other goods as a mark of our merit or virtue.
Aristotle argues that the best life is not devoted to honor. Here is the main passage where Aristotle argue for this:
A consideration of the prominent types of life shows that people of superior refinement and of active disposition identify happiness with honour; for this is, roughly speaking, the end of the political life. But it seems too superficial to be what we are looking for, since it is thought to depend on those who bestow honour rather than on him who receives it, but the good we divine to be something proper to a man and not easily taken from him. Further, men seem to pursue honour in order that they may be assured of their goodness; at least it is by men of practical wisdom that they seek to be honoured, and among those who know them, and on the ground of their virtue; clearly, then, according to them, at any rate, virtue is better.
I see Aristotle as making several points against pursuing honor or glory. The first is that whether we are honored or glorified depends upon others' opinions of us, which can be fickle. (Think of all those reality TV stars that have been so quickly forgotten!) Honor and glory are therefore not very reliable or stable goods. Moreover, honor and glory are not, Aristotle says, "proper" to us. That we are honored or glorified by others tells us what others are like — what they believe is good or virtuous — but only indirectly what we are like. And it seems likely that others can accord us honor and glory for the wrong reasons. In the end, Aristotle argues, what we want is not to be honored and glorified for our virtue but really to be virtuous.
I'm inclined to think Aristotle is right: Honor and glory are not inherently or unconditionally good. They are good only to the extent that we are honored and glorified for attributes or accomplishments that are genuinely good or worthwhile. That said, it's important not to exaggerate Aristotle's conclusions though. We shouldn't conclude that glory and honor are bad or worthless altogether. As social creatures, we need the recognition or esteem of others. Presumably the best life is one where we are honored or glorified by others because of our genuinely valuable attributes or accomplishments. Glory, we might say, is the icing on the cake only if the cake is actually a good cake.