This is the natural complement to the post about what to do when you have too many consonants. As mentioned before, if you dump one of your vowels, assuming that you are picking from the 144-letter Bananagrams distribution, you have an 8% chance of getting three vowels back. In my experience, if you have one extra vowel tile, and you just can't rearrange the grid to fit it in somewhere, even exchanging it for two vowels and a consonant tends to be easier to deal with. Of course, you could wind up with some consonants that are tricky to use (which may be why I rarely dump letters.. I also enjoy rearranging the grid).
Whatever approach you choose, you definitely want to know some words with a large percentage of vowels. There are some nice all-vowel words out there like aye, eye, and you. Here is a sampling of some longer vowel-heavy words:
eunoia (83% vowels)
eerie, adieu, audio, bayou (80%)
year, ooze, area, iota, auto (75%)
"Eunoia" and "sequoia" are also distinctive for being two of the shortest word containing all five vowels. "Eunoia" may get you in trouble if you try to use it since it's an obscure word. [I am partial to it because it is a brain word. It comes from a Greek word meaning "beautiful/favorable thinking". The "beautiful thinking" interpretation led to the obscure English usage of "eunoia" - a state of normal mental health. A stricter reading suggests that the Greek word referred to thinking that was favorable to someone (like one's spouse). The "blissful and benevolent state of mind" interpretation, though questionable, is the nicest.]
If you are interested in obscure words on the extremes of human language, check out the All-Vowel Words and All-Consonant Words dictionaries. They start with tame words like "eau" and "brr" and then spin off into highly arcane references (at times approaching Borges-level bizarreness). They come packaged together in a book called "Wye's Dictionary of Improbable Words", downloadable from Lulu for ~$14 or buyable from Amazon for $25.