This is a mighty wide question and specific answers would require a more specific question. Russia is a polity that has been in existence in one way or another for over a thousand years and you can imagine how various different dispositions can fit into that era.

That said I could conjure up some small answer in regards of European sentiment in very broad strokes. The predecessor of Russia, the Grand Principality of Moscow, was released from Mongol suzerainty in the late 1500's and thus began its more active expansionary phase. Even though Russia wasn't completely separate from rest of Europe under Golden Horde vassalage, it still had a more wary attitude concerning foreign influences and thus stayed relatively closed in that period. The Livonian War in the 16th century hailed an age of more active Russia and thus it became more involved with the Central and North European powers, first and foremost with Grand Duchy of Lithuania, Poland and Sweden.

As per usual in wars, propaganda is used as a weapon. Poland and Lithuania wanted to present themselves as the bulwark of civilization against "The Muscovite", a mantle that was later embraced by Sweden. Russia was presented as a barbaric, backwater nation, whose inhabitants are cunning, but ugly and coward-like. Muscovy was seen as an Asiatic despotate, ready to sweep over the civilized Europe. The Russians were also compared to the germanic barbarians from the Migration period. Taking to the account the fact that the Eurasian steppe had been a home to many invading nomadic hordes, such as the Huns, the Magyars and the Mongolians, this comparison was not too difficult to make. The expansive nature of the newly founded Tsardom of Russia was seen as a disturbing development by its neighbours, despite the fact that the ambitions of Polish-Lithuanian bloc and Sweden were not altogether different.

One of the first European writings concerning Russians was Sigmund von Herberstein's Rerum Moscovitiarum Commentarii from 1549 that in one hand served to make Russia more familiar in the west, but on the other hand fostered the stereotypes spoken earlier. The Russians were at the same time kind-hearted and brave, conniving and deceitful. More decidedly Russophobic accounts of La Russie en 1839 (1839) and The Will of Peter the Great (1812) continued to spread this familiar Anti-Russian sentiment. La Russie en was appalled of Russian autocracy and an alleged slavish mentality of the Russian people. The Will on the other hand is an interesting piece of prose.

And prose it certainly is, for the Will is a forgery, possibly produced in Poland and popularized in Napoleonic France. The Will presents a plan made by Peter the Great, where whole Europe is to be brought under Russian rule. Even though the expansionary nature of the Empire by that point might have given some credence to this conspiracy, it was still declared as a forgery in the early 20th century. As an off-topic remark, it is interesting to note how this forgery bears some similarity to The Protocols of the Elders of Zion, a later antisemitic forgery produced in 20th century Russia.

As a closing, and a kind of comical, note I want to introduce some comical-political maps from the late 19th century. The first one is a map by Fred Rose from year 1877. As we can see, European nations are presented here in more or less humorous fashion, and not always in a flattering tone. Again, the somewhat scary, unsettling and expansionary image of Russia is presented here in the form of an octopus, ready to spread its tentacles all over Europe. However, an alternative version of this map from the same year was also made by Fred Rose. In this one we take the role of the Russians, who are seen to stab the Turkish sultan in the form of Alexander II.

Russophobic sentiment wasn't all there is, however, and especially in the 19th century Russophilia started to take root in the minds of the European conservatives. The firm authoritarian hand of the Russian Emperor seemed reassuring in the nationalist and socialist turmoil of the 1800s, a sentiment which is quite well echoed in the alternative map of Fred Rose.

Source:

Immonen, Kari: Kyllä ryssästä saa puhua...Neuvostoliitto suomalaisuudessa julkisuudessa ja kirjat julkisuuden muotona 1918-39 (1987) [In Finnish]

Pictures:

http://www.bl.uk/learning/images/ideas/octopus-lg.jpg

http://timbryars.tumblr.com/post/66884446221/the-avenger-not-the-octopus-fred-roses-other

Edit: words, formatting.

It depends on who you are asking.

From the Southwest, the Russian's were seen as imperialist threats to the Iranian Qajar Dynasty. While European-educated scholars and civil servants in the Middle East* would be inspired by certain philosophies of pre-Bolshevik Russians, most in the region did not think of "liberty for the people" when first thinking of Russia. I will use Iran in the late 19th-early 20th centuries as an example.

Iran had already experienced multiple small conflicts with imperial Russian by 1910. In addition to worries from the north, the Iranian government was also aware of attempts by the British to develop spheres of influence in the southern portion of Iran. Russia already had a notorious reputation in the region for meddling with the Ottoman Empire (notably, on the excuse of acting in the interest of Orthodox Christians within the Ottoman Empire that wanted access to shrines in Jerusalem). Therefore large segments of the Middle East held a sense of distrust about European powers.

The Iranians would eventually move the capitol to the northern city of Tehran near areas of Russian influence. This was part of a strategy Historians call defensive developmentalism. Iran was experiencing a series of reforms to strengthen and centralize government in order to keep a closer eye on Russia. In this period you can also observe patterns of defensive developmentalism occurring in Egypt and the Ottoman Empire.

*Pre-World War I, the term Middle East was not commonly used and would be considered an anachronism. For the purpose of this post, I refer to the term which we are familiar to discuss the region from Morocco in the West to Iran in the East.

A couple of substantial answers have already been provided, noting the easy disdain that the West felt for the Russians. Allow me, nonetheless, to add to this by quoting the observations of the English poet George Turberville (c. 1540 - c. 1597), who accompanied Thomas Randolph (1523 - 1590), English ambassador to the court of Ivan the Terrible, to Muscovy in 1568:

The cold is rare, the people rude, the prince so full of pride,

The realm so stored with monks and nuns, and priests on every side,

The manners are so Turkey like, the men so full of guile,

The women wanton, Temples stuft with idols that defile

The seats that sacred ought to be, the customs are so quaint,

As if I would describe the whole, I fear my pen would faint.

Wild Irish are as civil as the Russies in their kind,

Hard choice which is the best of both, each bloody, rude and blind.

(Quoted in Richard S. Dunn, The Age of Religious Wars, 1559-1715, New York: W. W. Norton & Company, 1979 (2004 South Asian edition used): p. 69.

A text on this topic (teeming with primary sources) that I would without hesitation recommend is this:

Lloyd E. Berry and Robert O. Crummey (eds.), Rude and Barbarous Kingdom: Russia in the Accounts of Sixteenth-Century English Voyagers, London, etc.: University of Wisconsin Press, 1968.

Parts of the book can be viewed for free on Google Books.