The biggest detriment to the handeling on a stock corolla is not the tire size, but the brand!
The stock Firstone FR680s are total and complete crap. (as well as the goodyears or whatever else they come with) They wander on the highway and have horrible traction in the rain. Every time I tried to pull out in heavy traffic in the rain with my firstones (5-speed) I would spin the tires unless I babied the clutch out.
You should actually be fine with a 185/65/14 which is what came on the LE and S models. I assume you have a CE, which came with the 175s. The 195s actaully stick out a bit, but I like them.
I reccomend the Dunlop SP Sport A2 for a low-cost all-season radial with great wet and dry traction. The tire comparison guide at
www.tirerack.com is great for comparing tires even if you don't buy from them. Also check out the tire review thread in the Hardcore/Tech Forum here, which is linked in the Master sticky of that forum.