I just tried to add a tag for "implementation-defined-behavior" on SO but I couldn't because of the 25 char limit. I had to resort to an abbreviation (implem.-defined-behavior), which is rather ugly and to some extent thwarts the purpose of tags, i.e. easy indexing.
Although I acknowledge that too long tag names could be unwieldy, sometimes there are technical terms that cannot be abbreviated in any useful way (especially when there is no widespread acronym).
Could an increase of that limit be considered?
This is to respond to all the comments addressed at me that were triggered by the recent news brought up by @Shog9 in his answer.
Shog9 announced that the limit was raised to 35 chars network-wide, thus some people asked me to accept his answer instead of that of hildred's.
Sorry but, no, I won't accept Shog9's answer. Although I find the change very welcome, I think it is still somehow a sort of a patch for the SE network as it has evolved. A complex system such as SE network is now could well afford another mechanism vetted by high rep users/mods on per-site basis.
I really welcome the change, but this solution would have satisfied me at the time I originally posted my question. After all, 35 chars is probably a reasonable limit for a site like SO, or EE.SE where I'm currently active and committed.
At that time, IRRC, the SE network was still very young and there were very few sites on the network that rivaled SO in quality and traffic.
But time has changed since then, and there are sites that have greatly improved and that have the potential of outperforming SO in traffic (after all, there are more people watching TV or practicing mountain walking than programmers out there!).
Given how SE network has evolved, I still think that the right, long term, solution is option #5 in hildred's answer: in short, allow much longer names under the supervision of mods and as a new privilege for high rep users.
Abuse is always a possibility, even with shorter tag names or for other facilities of the sites. I don't see why, apart from some technical reason related to the structure of the system, hildred's solution (or kind of) could not be implemented with the same level of safety/security as other facilities.
There are sites, as it was shown by others, that desperately need a much higher tag length limit, if tags are to be useful for them.
As the name of something increases in length, meaningful abbreviations start to become unintuitive and not unique, hence you cannot expect people to gain any convenience when searching for an abbreviation they don't know about or that they must guess.
In the end, as on of those sites grows, the problem becomes ever worse, because funny abbreviations, with lots of still funnier synonyms, increase, rendering the tag system unreliable and inconvenient.