(Classical) Latin nouns have one of 3 genders (masculine, feminine, and neuter), and each noun has 12 possible forms (6 cases * 2 numbers); pronouns follow similar rules; and the adjectives modifying a noun have to agree with it in case, gender, and number (so typically a single adjective has 36 possible forms). Verbs vary by voice (active/passive), mood (indicative, subjunctive, imperative, infinitive, participle, gerund, supine), tense (different moods have different numbers of tenses, with 6 for the indicative), number (singular or plural), and person (3 persons); overall, a single verb will have more than a hundred different forms.
Because verbs have so many specific forms, it is also pretty common in Latin, as in most modern Romance languages, to omit the subject of a sentence, as it can typically be inferred from context plus the specific verb form - so, you often have to recognize the verb form to be able to understand who the sentence is even talking about (e.g. a sentence might say "amo regem"; if you recognize the words but not the specific forms, this means "love king"; but this unambiguously means "I love the king").
Now, there is quite a bit of regularity here - there are 5 categories of regular verbs (plus some specific irregular verbs), and 5 categories of nouns (though there are multiple sub-categories, as there is some variation in noun forms even in the same category; plus of course some irregular nouns).
Overall no, I don't see any comparison where you could say that Latin is a simple language. All modern Romance languages have universally merged or dropped various of these features. For example, Spanish drops the case system entirely, drops the neuter gender, and reduces the number of moods for verbs.
> All modern Romance languages have universally merged or dropped various of these features.
Wikipedia informs me that Romanian is a Romance language and has retained some of it. Also, the Slavic languages have largely retained most or all of what you’re describing, although they are not classified as Romance languages.
I am a Romanian native, so I know quite a bit about it :D . Romanian has kept the major features, but it still dropped a lot. For example, instead of 6 noun cases, Romanian only has 3, of which only 2 are commonly used (the third, vocative - "hey, you, bird!" - is quite rarely needed; and even when it is, it's usually replaced with the nominative by most speakers - we commonly say "pisica rea!" instead of "pisico rea!" for "bad cat!"). There are also fewer verb tenses in Romanian than Classical Latin, and some are formed with auxiliary verbs instead of being truly separate verb forms. Also, the neuter gender, while technically existing in Romanian nouns, is simply masculine in the singular and feminine in the plural, there is no unique third form for adjectives or articles.
Slavic languages also have a case system (I think it's possible that this is part of why Romanian kept the Latin case system, as there was quite a bit of Slavic influence in Romanian), but they didn't "retain" it from Latin, as they are not Romance languages at all - they simply share this linguistic feature; Latin and Old Slavonic are by no means the only languages with a case system.
O-S-T-MUS-TIS-NT!!