Every year at the beginning of the spring, I do preliminary hikes and do some light maintenance (removing broken tree from the trail etc...) but this question made me realize to what extend should I maintain the trail? And if some actions could be considered as inappropriate?
It's always OK to move fallen debris from the trail, assuming you are sure you are on a real official trail. Make sure you don't accidentally remove "brushed in" trail entrances. That is where brush was deliberately piled so that a trail is not used, hopefully eventually reverting to just woods again. If you're on anything with clearly deliberate blazes, you're safe.
For anything more than clearing debris without tools, you need to ask the owner or administrating agency. Public agencies usually have rules that they don't want any unauthorized trail work. This is just to make sure they don't get morons doing stupid things and to avoid liability. If you get to know the manager, forester, committee, or whatever that oversees a particularly area and they get to know and trust you, you usually end up with a informal arrangement where they trust you doing trail work without asking first and without them formally giving permission.
Some groups can be real control freaks and don't want anyone, even those that clearly know what they are doing, doing trail work without 3 levels of approval. I know one organization that takes this to the extreme. They have a "steward" assigned to each property, and then a few master stewards for groups of properties. Even though I actually built some of their trails, I can't go out there when I have a spare hour and clean up a trail without prior approval. I don't feel I should work that hard to give away my time for free, so I find a different place to do trail work. There are plenty of places run by other groups or organizations that are happy to have me help.
I'm on the trails committee in my town, so I am actually authorized to go out with a chain saw and clean up a mess on any of the town land whenever I see a need. However, we don't want people going so far as using a chain saw without talking to us first, but even then there are certain individuals and groups we know aren't going to make a mess and nobody is going to make a fuss about one of them going out and clearing a major blow-down. But, we're not going to tell you that if you come and ask as a individual, especially if we don't know you.
A good way to get known is to volunteer for organized trail work. I don't know how other towns work but we probably have 1-3 formally organized events a month except when the snow it too deep to do much useful. After you show up a few times, the organizers will recognize you and you'll be trusted a lot more. You might even mention a particular trail you think needs some work and offer to take care of it over the next week or two. Once you're known, you'll probably get a quiet unofficial nod and it works out for everyone.
A good example illustrating the issues envolved came up last night at the town Trails Committe (of which I am a appointed member) meeting. We learned that someone or some group has gone out to several trails with a leaf blower and "cleaned" them off down to bare ground. We're pretty sure it was the local mountain bikers club, or at least individuals from there. We have a generally good relationship with the mountain bikers, and they show up regularly to help out with scheduled official trail work. We don't really want to get in anyone's face about this, but would rather the leaf blowing wasn't happening, at least not without prior approval. The problem is that this promotes erosion, and also gives the trail a unnatural and less wilderness feel. We also really don't like anyone working on trails with powered tools without coordinating with us first.
It's too soon to tell how this will be resolved. Some polite off the record conversations will be had with those envolved, and that will probably resolve this issue. This is a small town, we pretty much know who is doing what, and we also understand they probably thought they were improving things. Mountain bikers don't like downed leaves because they can be slippery and cover up hazards.
In any case, this illustrates some of the problems you may create for other people when doing what you think is helpful trail work. I'd say catagorically to never go so far as using powered tools (chainsaw, weed whacker, brush mower, leaf blower, etc) without getting the proper permission first. Picking up trail debris and even pruning back small overhanging limbs with a hand clipper would be OK in most cases. Everything in between is a gray area where you should first at least know who the owners or managers are, what rules there might be, etc.
As a general rule in the US
If you want to help maintain trails, its usually better to volunteer with an existing organization with a relationship with the park, than to try and act on your own. Its not always going to be possible to know what the exact appropriate / inappropriate line is when you're out on your own hiking.
Sometimes park services have conflicting priorities (for instance, balancing the needs of hikers with mandates to protect the natural environment, or balancing the needs of hikers with rock climbers or mountain bikers). Individuals that perform large, impactful "improvement" projects can aggrevate tensions within the park in a way that planned volunteer events don't.
Removing broken treebranches from a trail by hand is probably fine, but much more than that (anything that would require tools, building systems of cairns, etc) should probably be left for formal trail improvements.