Vowel changes can move in pretty much any direction. The only rule is that they have to move gradually; /a/ is not going to become /i/ without some route in between, such as moving through /ɛ/ and /e/.
There are also general trends with the vowel inventory:
1) Most languages have an open vowel (/a/, /ɑ/ or in-between)
2) Most languages have /i/.
2) For every front vowel (except open vowels), there is usually a back vowel at the same height. If a language has /e/, it tends to have /o/ as well. Because most languages have /i/, this therefore means that /u/ is common as well.
Another factor is that consonants can affect vowels too. The obvious ones are /j/ and /w/. Other palatal consonants can also introduce /i/ and /ɪ/ or move vowels towards those sounds. Likewise, other labial consonants can introduce rounded vowels.