;-; I had no idea it had already be done. Is it OK if I still use the idea Chili/Gimmie? I'll be making it my own and ignoring that wiki page entirely XD.
Some servants have more than one NP, but in general there is one. In the anime at least, very few characters have more than on NP, however they might have different ways to use it/techniques/abilities.
Characters such as Saber have one main NP, Excalibur, but then has Avalon which is kind of an add on. The Lancer in /Zero also has two NPs.
Actually the only franchise which has mainly one-Phantasm Servants is the Fate/extra game, and that's likely due to programming/balancing limitations for a fighting game; in F/sn Saber has Excalibur, which is an all-out offensive option, but also has Invisible Air, a Noble Phantasm that, in addition to concealing Excalibur, also serves lower-end offensive option which grants further utility as a speed boost (because revealing the identity of Excalibur means revealing the Servant's own identity as well, Saber uses Invisible Air to beat up weaker people). Avalon isn't just an add-on, either, as it's a very powerful defensive Noble Phantasm that gives ridiculous amounts of regeneration and heals otherwise fatal wounds.
F/sn Lancer has 2, which is pretty standard (well, same weapon with 2 different attack forms, but classified as 2 separate Phantasms nonetheless); for some other examples, Gilgamesh as Archer has 3 different Phantasms, two of them being ridiculously broken (Gate of Babylon is basically as good as Unlimited Blade Works! ... if you don't count the Reality Marble component, but Gate doesn't rank down stuff; and Ea is, well, it beats everything if it gets used). EMIYA as Archer has basically infinite Noble Phantasms (even though Unlimited Blade Works is totally hax), but even if we discount the multitude of modified and standard Broken Phantasm projections we can still loosely count Kanshou and Bakuya in addition to UBW itself, because Crane Wing Three Realm is a special technique. F/sn Rider has 3, Caster -technically- has 2 (only Rule Breaker is really usable - and it's very good - but it doesn't matter that much because her magic is pretty strong compared to modern magecraft), and Berserker has 2 (so that's 6/7 Servants with 2+ Noble Phantasms).
If we examine F/z: Saber is the same, Lancer here has 2 actually different Phantasms, Berserker has 3, Assassin has 1 as normal for the class, Caster, as an irregularity, has only 1, Rider has 2, Gilgamesh is the Archer here and is also the same, and that's it.
Plus there's a lot of customization to be had with Combat Skills.
My hypothesis is that the reason for Assassin not typically having more than Noble Phantasm is twofold: one, the Fuyuki War places restrictions on the identity of Assassin, which forces his/her Noble Phantasm to be Zabaniya, and two, the Assassin class has pretty terrible parameters in general. Outside the Fuyuki Wars in the F/apocrypha light novels, Assassin of Black (Jack the Ripper) does have two known Noble Phantasms already, so. (We'll have to wait until the full info books are released to know all the abilities of all the Servants for it, and I think Semiramis would likely have at least two as well, but not much has been revealed ... yet.)
The purpose of this speech was to, well, clarify the fact that Servants don't need to stick to one Noble Phantasm in canon (and usually don't, since most spirits that become Heroic Spirits do so because they were immensely powerful in life); please don't take it as a personal attack on anyone! Okay thanks bye.
(Side note: I don't really like the F/sn anime adaptation ... it kind of mix-and-matches material from each of the three routes and is just generally unsatisfying. F/z anime adaptation was very good though!)
(Other side note: Lu Bu!
https://typemoon.wikia.com/wiki/Berserker_(Fate/Extra_Rin_route))