Pronunciations are usually highly dependent of the particular romanization used: pīnyīn, Wade-Giles, the old Chinese postal system romanization, or idiosyncratic romanizations.
If you're asking about specifically pīnyīn's ‹j, q, x›, they're in general terms read in whatever way these three letters are pronounced in the languages in question.
This means that in English, ‹j› is usually [dʒ] as in "jam", ‹q› is [k] as in cake, ‹x› is [ks] as in sphinx. "Beijing" is a notable exception—many people pronounce it with a [ʒ] sound like the ‹s› in "pleasure" as an artificial foreignization, basically identifying it with French. Many others do pronounce it with a [dʒ] sound as in "jam" though.
In French, ‹j› is [ʒ], ‹q› is [k] and ‹x› is [ks] as Nouus-rxf explained.
In Spanish it depends a lot on the familiarity with a name and if the person knows a little Mandarin or not... In names you hear a lot in media like "Beijing" and "Hu Jintao", the ‹j› is pronounced with /ʝ/: /bei.ˈʝing, ˈxu ʝin.ˈta.o/. As you Ghabi may know already, /ʝ/ varies quite a bit per region, some would use [ʝ], others [j] or [dʒ] in these two examples. I've no idea how people from the Río de la Plata do it considering their /ʝ/ is [ʃ]—I'll open a thread in the Spanish forum. Many would pronounce a ‹j› as /x/ when encountering a name with itthough, but then again, as a Spanish speaker you practically never encounter the necessity to read names like "Jilin", and if you do you probably know some Mandarin anyway. ‹q› is usually [k] and ‹x› is [s] or [ks].
(I wonder if there's anybody else in the world who pronounces ‹Xiangqi› as [ˈsiantsi] like I do instead of [ˈ(k)siaŋki]...)