This is an awfully broad question. For example, what Europeans? Rarely anyone at the time identified with a nation state and certainly not as Europeans, that is a late invention. Either way you'll get different answers depending on who you ask.
In Sweden's case it was a constant rivalry (before Russia, Novgorod was the main competition) and border conflicts/wars. Much of it had to do with gaining access to the Baltic and controlling trade/taxation. This was the idea of Dominum maris baltici which later on would guide much of Swedish foreign policy.
From a Swedish perspective Russia was regarded both as a familiar entity in the form of a constant enemy* but also as something very foreign, a country more similar to Asiatic kingdoms than to Western European early states. For example, have a look at the coat of arms of [Karelia] (http://www.rusi.info/images/Karjalanvaakuna.jpg). Symbolizing the border of "Western/Eastern" with the crooked blade to the east.
