The time between arrest and being presented to a judge depends on the country you are in:
You can be in jail for 23 days before you even see a judge and are charged, and that clock resets whenever they officially start to investigate you for a different possible charge. You are not charged, you are just accused of this related and greater crime. This tactic even has a special name: Hitojichi shihō. Someone they want to investigate for murder can be first imprisoned to investigate the deposit of the corpse, then for the actual murder, for a total of 46 days maximum - and if the DA isn't creative to get some other lesser included charges in. Against some Yakuza, some DAs allegedly managed to chain up much more.
However, those 23 days (per investigation) are all the pre-trial investigative confinement that the state gets before a trial - the moment the formal charge is entered, the trial has to begin soon after... However, the state also often has the arrestee's confession at that point - partially because a creative DA might manage to keep you nigh permanently and in part because you don't have the right to have your attorney at your side during questioning in Japan. This is partially the reason why Japanese courts have such a crazy high conviction rate: more than 99% of the cases brought by DAs are convictions, in most cases using the confession obtained in the pre-charge detention as a piece of key evidence.
If you are a suspect of terrorism and emergency powers are invoked, you can be kept for up to 28 days before you need to be either charged or released. Rick mentions 14, which is the norm for terrorism suspects. However, the law was updated since 2005 to allow those 28 days when emergency powers are invoked. See Justice for more information. Generally, the time limit is 72 hours, or 96 hours for serious crimes, starting at the arrest hours, apply.
The EU has the European Convention on Human Rights (Art. 5 III):
Everyone arrested or detained in accordance with the
provisions of paragraph 1 (c) of this Article shall be brought
promptly before a judge or other officer authorised by law to
exercise judicial power and shall be entitled to trial within a
reasonable time or to release pending trial. Release may be
conditioned by guarantees to appear for trial.
However, what is Promptly is dependant on what the countries implementing say it is. As an example, let's take a (closer) look at Germany.
While you can be in investigative confinement (Untersuchungshaft / U-Haft) for months or up to a year typically, you need to be already officially charged and a judge has to affirm you are in U-Haft. This decision that you need to be in confinement needs to be repeated regularily in case of long investigative confinements. This Investigative Confinement, "Untersuchungshaft", is defined in STPO §112 (~process regulations for criminal trials), and usually is limited to about 6 months before the suspect is to be released or be at trial, but in extremely difficult cases it can be extended by special motion in the layer of Oberlandesgericht, which is about the highest state court. Still, while an extension to 9 or 12 months is possible, there can be cases where this may be extended even further, even if that might not be entirely correct on other grounds - there had been appeals to the European court for human rights about such.
On the other hand, once a trial starts and the court sees a flight risk or that you might pose a potential danger, you stay in (or are taken into) Untersuchungshaft for the duration of the trial. That is different from pre-trial Untersuchungshaft, in that you can't appeal on that your trial didn't start yet. In either case of Untersuchungshaft, any and all confinement is counted as time served, like the case of Fritz Teufel. In his case, his trial was seriously delayed and he was in Untersuchungshaft for 5 years before they convicted him to 5 years. In the end, he had already served all the due time due to the investigatory confinement, so he was released almost on the spot - just a little bit of paperwork and he was out..
Now, that is all court-ordered confinement. How far can we get without the court? What does Germany count as prompt?
So, unless you have been put into investigative confinement by court order, you have to be released at the end of the day after you were arrested. End of the day is defined as midnight by the general rules. So if you were arrested Monday, 1st of January at 00:01, you are to be released on Tuesday, 2nd of January, 24:00. So, the absolute maximum confinement outside of the daylight-saving change day is 47 hours 59 minutes and 59 seconds until you need to have been seen by a judge, but because it is nigh impossible to get to see a judge between 16:00 and 24:00, the typical confinement till you are formally charged and possibly transferred to Untersuchungshaft is usually less. On a mere technicality, there is one day a year where you might be confined twice from 2 AM to 3 AM, but that is also always a Sunday.
