I want to know if there are other parts of speech -other than particles- in other languages than English or other Romance/Germanic languages.
The most important message is that about one dozen parts of speech seem to be sufficient for part-of-speech (POS) tagging. Additional markers often include things not classically regarded as parts of speech, such as punctuation, symbols (e.g., for Twitter corpora!) and a "residual" container class for everything else.
There is some disagreement about the content of some classes: Traditionally, pronouns include pronomial adverbs and adjectives. A modern school takes the pronomial adjectives out of the pronoun class and names them determiners (and often, the classical articles are put there, too) and classifies the pronomial adverbs (e.g., "how") just as adverbs.
There are several attempts to unify POS over languages, and here are some them:
EAGLES: http://www.ilc.cnr.it/EAGLES96/pub/eagles/corpora/annotate.ps.gz EAGLES Recommendations for the morphosyntactic annotation of corpora, ''Obligatory attributes/values, Major Categories'', §4.2.1 on page 7
STTS/HW: http://www.sfs.uni-tuebingen.de/resources/stts-1999.pdf Guidelines für das Tagging deutscher Textcorpora mit STTS (Kleines und großes Tagset), ''Hauptwortarten'', Tabelle 2.1 on page 4
TANL: http://medialab.di.unipi.it/wiki/Tanl_POS_Tagset#Coarse-grained_tags Tanl Coarse Grained Tags
UD-17: http://universaldependencies.github.io/docs/u/pos/all.html Universal Dependencies
UP-12: http://www.petrovi.de/data/universal.pdf Universal POS 2nd paragraph in the right hand column of page 2
The summary table below shows the tags drawn from the tag sets quoted above (in their original spelling).
||= EAGLES =||= STTS/HW =||= TANL=||= UP-12 =||= UD-17 =||= Notes =|| || N || N || S || NOUN || NOUN || noun || || || || || || PROPN || proper noun/named entity || || V || V || V || VERB || VERB || verb || || || || || || AUX || auxiliary verb (includes modal auxiliaries like ''should'' or ''must'') || || AJ || ADJ || A || ADJ || ADJ || adjective || || PD || P || || || || pronoun/determiner (as one single class) || || AT || ART || R || || || article || || || || D || DET || DET || determiner || || || || T || || || predeterminer (e.g., '''tutto''' il giorno) || || || P || PRON || PRON || pronoun || || AV || ADV || B || ADV || ADV || adverb || || AP || AP || E || ADP || ADP || adposition (circum-, pre-, postposition) || || C || KO || C || CONJ || CONJ || conjunction || || || || || || SCONJ || subordinating conjunction || || NU || CARD || N || NUM || NUM || numeral; cardinal numeral (ordinals are tagged as adjectives or adverbs) || || I || ITJ || I || || INTJ || interjection || || U || PTK || || PRT || PART || unique; particle || || R || || X || X || X || residual; other || || || || || || SYM || symbol ($, %, §, ©, +, −, 😝, !http://example.org, !firstname.lastname@example.org) || || PU || || F || . || PUNCT || punctuation || || 13 || 11 || 14 || 12 || 17 || total number of tags ||
STTS/HW lacks generic tags for punctuation and other: They could be supplemented as $ (for punctuation) and X (for other)
UP-12 lacks a tag for interjection; interjections are mapped to the class X
UP-12 and UD-17 lack a tag for article, it is absorbed into the determiner class.
TANL lacks the category particle, the Italian negation particle ''non'' is classified as an adverb.
TANL considers article, determiner, predeterminer, and pronoun as first-class citizens in parts-of-speech.
The problem with this question is that parts of speech are just a construct used for the description of language - not necessarily a real thing in a language. You can see that across languages only nouns and verbs are fairly uncontroversially universal with adjectives being another good but still disputed candidate (See Dixon's Basic Linguistic Theory).
So if you were starting with a different language you might be surprised by things like determiners in the languages you list or prepositions. Other languages may have various classifiers that may seem a bit strange. There are other things that represent a distinct category but do not make it as a part of speech like quantifiers. Even in English, you will find lists ranging between 8 and 11 different parts of speech depending on the authors' perspective and need.
You will also find a lot of variations in the internal typology of parts of speech across languages. So Czech pronouns and English pronouns or adjectives will come out looking quite different (e.g. Czech possessive adjectives).
After a quick scan of the paper A Common Parts-of-Speech Tagset Framework for Indian Languages, nothing stood out as particularly distinct from the POS of European languages. However, on running over a chapter from Antony's thesis on Kannada, I noticed two categories I have not seen in most European languages: echo words, and reduplication. Finnish and Hungarian seem to have these two categories of words.
On second thought, English seems to have echo words too (teensy-weensy, itty-bitty, higgledy-piggledy, etc.) but I have not come across POS tag sets that recognize these as a separate category, probably because there are just a handful of such expressions in English. In contrast, in Indian languages, these POS categories are open classes.
English has: noun, pronoun, adjective, verb, adverb, preposition, conjunction, interjection, particle (yes, no, to), article.
English has several forms of verb that can be considered parts of speech depending on viewpoint: present participle, past participle, gerund.
Russian does not have articles, but has participle and transgressive. Both described as a form of a verb in English Wikipedia (English also has participles), but in Russian linguistics they are considered separate parts of speech.
German language has another form of verb, known as "inflective". This can also be viewed as a separate part of speech depending on viewpoint. In Russian such words are considered interjections.
Some languages (including English and Latin) have clitics, which are sometimes classified as parts of speech, but I prefer to count them as parts or word (morphemes) that come after ending (prefix(es)-root-suffix(es)-ending-clitic). In Russian clitics (-де) are classified as particles.