I had Latin in school, though I never was very good at it. But when I first saw Russian grammar, what I immediately thought was 'hey, that looks like Diet Latin'.

Verb conjugation is almost the same. It's just that Russian has lost most of the tenses, but what remains looks much like Latin.

to carry, I carry, you carry, he carries, we carry, you carry, they carry
ferre, fero, fers, fert, ferimus, fertis, ferunt
нести, несу, несёшь, несёт, несём,несёте, несут

To me these look very similar. A non-root vowel ends the first person singular, a similar one the third person plural, but is absent from the other forms. There is someting 2nd person singulary about using a sibilant (s, ш) a t in third person singular, an m to imply 'we', a tis / te to imply 2nd person plural, etc. Enough evidence to see a common root, if you ask me.

Of course similar influence can be seen elsewhere:

French: je porte, tu portes, il porte, nous portons, vous portez, ils portent
Spanish: yo llevo, tu llevas, el lleva, nosotros llevamos, vosotros llevais, ellos levan
Italian: io porto, tu porti, lui porta, noi portiamo, voi portate, loro portano

But if you compare that with English above or German, then you see a clearer difference, so I would say that coming from such languages, Russian definitely looks closer to the Roman languages than to the Germanic ones at least:

ich trage, du trägst, er trägt, wir tragen, ihr tragt, sie tragen.

Of course it is true that all Indo-European languages come from a heavily inflected root language. The oldest known member of the family is Sanskrit, which had a whopping 792 distinct forms for each verb according to Frederick Bodmer. We should all be happy that the tendency to simplify on the inflection is in all our languages.

And Russian has interesting features, too, not found in Latin or other Roman languages, such as marking number in the past tense but not the person, but marking gender.

Robin