One way of summarizing the characteristics of a given language, as well as to compare one language to another, is the index of synthesis: a measure of the degree of synthesis - the process of combining multiple units of meaning into smaller numbers of words - in a language. Thus, in other words, the index of synthesis is a measure of how much information is contained in each word.
The index of synthesis ranges from isolating to synthetic. Isolating languages contain exactly one unit of meaning per word, and adding additional meaning to some word requires adding other words that modify it. On the other end, a purely synthetic language (not known to exist), would have one word for each entire sentence.
English has been changing in favor of isolation for the last couple thousand years, and Modern English is close to the isolating end of the spectrum, with many words containing single units of meaning. Off the top of my head, I'm going to say English words other than nouns, pronouns, and verbs are isolating; for example, adjectives and prepositions contain only a single unit of meaning in each word. Verbs are becoming increasingly isolating, adding auxiliary verbs to indicate additional meaning to the base verb (e.g. 'should not have seen'). Nouns are also becoming less synthetic, as there are now only two flavors of most nouns: singular objective (e.g. 'cat'), and plural objective/possessive ('cats', 'cat's', and 'cats'', which are all pronounced the same when spoken).*
The romance languages are a little more synthetic than English. Spanish, for example, maintains distinctions between singular and plural, male and female (four forms total) in both nouns and adjectives; for example, 'gordo', 'gorda', 'gordos', and 'gordas' all mean the adjective 'fat', but they indicate singular male, singular female, plural male, and plural female, respectively. Spanish also contains more information in its verbs, chiefly the animacy level and number (singular/plural) of the subject.
Japanese is much further toward the synthetic end. In Japanese, some word types commonly undergo agglutination (agglutination and fusion are the two types of synthesis): the combining of multiple "independent" words into single words, when the context calls for it. For example, the pronoun 'watashi' ('me') can be fused with the suffix '-tachi' to form 'watashitachi' ('us'). Verbs are also fused with auxiliary verbs, commonly meaning things like the passive voice, causation, negation, or politeness; for example, the nine-syllable monstrosity 'kokoruminiawasezu' is formed from either 'kokorumi' ('trial') or 'kokorumiru' ('to test'; I'm not sure if this is the noun or verb, as they're both identical when agglutinated), 'niau' ('to suit; to match; to become; to be like'), '[sa]seru' ('cause to'), and 'zu' ('not'), from the Lord's Prayer meaning 'lead us not into temptation' (that's the popular archaic version of that line, but a more accurate Modern English version would be 'do not test us/our faith', which is closer to the Japanese version). As well, multiple types of words may be fused together, as in 'shakugan', formed from 'shaku' (this appears to be an abbreviation of 'shakuretsu', meaning 'burning') and 'gan' ('eye[s]'), from an anime called Shakugan no Shana ("Shana of the Burning Eyes").
A Turkish example from Wikipedia illustrates extreme levels of synthesis: 'Çekoslovakyalılaştıramadıklarımızdanmışsınız' (18 syllables, if I counted correctly), meaning "You are said to be one of those that we couldn't manage to convert to a Czechoslovak". Some people believe that Turkish is related to Japanese (the Altaic hypothesis), but this has not been conclusively proven.
* While English may have [sometimes large] agglutinated words such as 'antidisestablishmentarianism' (an agglutination of 'anti-', 'dis-', 'establish', '-ment', '-ary', '-an', and '-ism'), these are generally considered separate words, and so are not considered to be a synthesis of smaller words; this classification is supported by the fact that such agglutinations cannot be made freely, but must be words established through common use. In contrast, Japanese verbs may be freely agglutinated with other verbs/words that make sense (e.g. auxiliary verbs), without creating entirely new words.