First, to clarify, English does have accents. For instance, jalapeño (with a tilde; note that in Spanish this word refers to any accent), naïve (with an umlaut or diaeresis), naïveté (with an umlaut and an acute accent), or voilà (with a grave accent). Use of the accent varies with these words, but they exist, and the more formal styles are scrupulous about using accents with these loanwords.
As mentioned in other answers, the theoretical use of accents in Spanish is to distinguish two words or to note stress. Thus, si (if) and sí (yes) or sí mismo (oneself) but only ti (e.g. ti mismo). That's also why video and vídeo are both used, depending on how the word is pronounced in given region: that is, viDEo or VIdeo. Particularly, words in Spanish have a "usual" pattern of stress, and if a word deviates from this pattern, it takes an accent.
However, the practical answer is that accents are not always necessary. Spanish speakers frequently omit them in informal writing (e.g. text messages or Internet writing). You wouldn't want to do any of this in formal writing, but it's pretty common and doesn't really hinder understanding.