After a quick search using the bab.la Swedish-English-Swedish database (thank you Patrick) it was concluded that 1558 words, terms, or acronyms are identical cognates (in spelling, but not necessary in meaning) in both the Swedish and English languages.
Words include country names such as England, Columbia, and Argentina, religion such as Baptism, Hinduism, Presbyterian and other more common terms such as liberal, pentagon, pilsner, Viking, accent, access, adapter, album, charter, dilemma, digital, donation, irritation, salt, socialist, tunnel, avocado tiger, and fusion along with many others. Most of these common words have Germanic, Latin or French roots; such as champagne, déjà vu or résumé.
However, it is also very important to note that one must not confuse cognates with false cognates such as bra (good in Swedish, women’s undergarment in English), full (drunk in Swedish, satisfied in hungry in English), kissa/kiss (to pee in Swedish, touching lips in English) and trosor/trouser (panties in Swedish and pants in English).
According to Bill Bryson’s book “Mother Tongue”, the English language contains about 200,000 words in common use, German about 184,000, French 100,000 and Swedish only 40,000. This means, to learn fluent Swedish you only have 38,442 more words to memorize!
For a complete list of all 1558 words, please see the attached word list: