It's always worthwhile to take some time to try to figure it out by yourself. But eventually there's a point where you're unsure how much more time it would take to figure it out by yourself (which could take far longer than you originally think), and when asking for help could be more helpful.
So for analytical or computational research, what are some guidelines for when you should ask for help (from either your adviser, other grad students, or other researchers) when you get stuck?
Answer
I find that grad students always wait too long to ask for help, either out of fear of looking "stupid", or out of inexperience, or out of a misplaced sense of stubbornness. If you've spent a few weeks on something and you're thoroughly stuck, then you should absolutely ask someone (advisor, other students, anyone with knowledge). You'd be surprised at how often you were merely barking up the wrong tree, or just didn't know a very important fact or reference, or just had to reformulate the question differently. All of this takes experience, and that's what an advisor is supposed to provide.
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