Is it good to upgrade the crossovers in your speakers?

I'll be contrary here and say go for it. As long as you're not changing values of components you're not going to change voicing to a huge degree. And the best quality parts are only going to improve timbre, natural sound quality. You can always go back to stock if you didn't like changes. Understand exactly what sound qualities you're looking to improve, do your research on parts you plan to upgrade. Get it right and you're speakers will be much improved.

I agree with sns, you can always go backward if a change is not in the right direction.  There are a lot of popular choices of current production parts that are not necessarily the way to go; vintage parts should not be overlooked even if the common wisdom is that they go bad with time.  Some of the best recent builds I’ve heard utilized such vintage caps as Western Electric paper-in-oil capacitors, Cornell Dublier caps, and Jupiter caps (not a secret, as many of these parts are ultra expensive).  Internal wire can also be quite important and the right choice can be hard to determine; a builder I know basically chooses between various types of Audio Note speaker wire, including crazy expensive Sogon wire.

I have rebuilt crossovers and wiring in two different speakers, and for the improvement made, looking back, I'm not sure that it was really worth it dollar for dollar. I spent the most on capacitors of course. Looking back, I think with what I know now I would change wiring and leave the rest alone unless there was a problem. My current two pair of speakers are both wired with what appears to be lamp cord, and I know that high quality wire with better insulation will give a better sonic result, so that's something I'm planning on doing soon.

Unless the caps are known to be inferior, I’d leave them alone.  You might stumble into what you perceive as an improvement, but you could also cause some damage, or end up  not liking the change as much as the originals.  

Ten years ago I had my vintage (1978) Large Advents and B&W 805 Matrixes (1997 or so) upgraded by John Van Leishout of Van L Speakerworks in Chicago. I pretty much gave him carte blanche within reason to upgrade everything. I know the caps, inductors, and internal wiring were replaced. The sound improvement was substantial in both sets of speakers. I recall that at some point he called me about various cap options for the B&W's ranging from $200 to $1500 per cap. I am pretty sure I told him to go with something in the $200-$300 range and that my "carte blanche" was not really blank. 

My recommendation is that if you are considering this truly for sound and not also for the fun of the exercise, than have a pro do the work.