travel bag is now an accepted answer, but it is a bit of a false friend, since many (most?) travel bags are not resväskor in Swedish. I recommend image googling resväska and travel bag and comparing the results. However, some travel bags are really resväskor, so we've decided to accept it.
In South African English, most people would use the word "travel bag". And a travel bag is a "bag that is used for travelling purposes". Personally I have never used the word Suitcase when speaking of a bag which I use for travelling.
Ikea uses the word "Travel bags" http://www.ikea.com/us/en/catalog/categories/departments/ikea_family_products/16248/
and one can search google images with search word "travel bag"
Well,in my language ruksak is what we call those bags that we use for school books mostly,i suppose it's a german/ic loan word.I mean those bags with two straps that you carry on your back.And i'm not sure about this but you might be thinking of ˝kofer˝ ,a big bag with wheels and a handle.I think that's a kofer,but i can't be sure that the word even exists in English,probably does in German
I guess the words have different connotations in different languages! This is what a rucksack generally is in English: http://i.imgur.com/a3N7Eq6.jpg
Usually for hiking or camping.
Kofer sounds like what I'd call a suitcase. Though a larger, travel suitcase, not the kind a businessman would carry to work. I can't think of a word that would differentiate the two, and Google isn't helping me there, outside of the generic word "luggage".
That (the image) is en ryggsäck in Swedish.
We have an old word en koffert but that's from before suitcases used to have wheels, so I'd say en koffert in Swedish is an old-fashioned suitcase in English. The kind you don't carry very far. For modern-day suitcases, we say resväska.