It all depends on your gauge in comparison with the original pattern. Assumming your gauge matched the gauge with the size 8 a bigger needle size would result in a bigger knitted item with the same amount of sts as the original. A smaller needle size would make the item smaller.
Say you are knitting a scarf that the gauge is 20 st x 24 row = 4" x 4" on size 8 needles. If you casted on 30 sts your scarf would be 6" wide.
If you switch to size 9 your gauge might become like 18 st x 21 row, therefore the 30 sts would make your scarf wider so about 6 2/3" wide.
And finally a smaller needle size, say a 7 would make a gauge of 23 st x 26 row, a 30 st scarf would be thinner so about 5 1/4" wide.
This is all assuming your gauge matched the original gauge with the original needle size. A lot of times a person's gauge is different and they will need to go up or down in needles sizes to get the correct gauge.