I've been strength training now for 10 weeks and have never bothered with spring collars because the weights have been light and the collars are a pain when doing 4 different warmup weights, then the work weight.
I'm getting to a stage now where the bar is starting to noticeably flex (280# reps deadlift, 265# reps squat on a 17.5kg bar), but still there is no sign of plates sliding. Nor have I found myself tilting the bar sufficiently to cause sliding. Because of the tight fit of the plates to the bar, I'm not even sure if they'd slide off if the bar was tilted at 45 deg (but I might just test that tomorrow).
Yet every time I find the person before me hasn't unloaded a bar, there are collars on them. Even if it's just 25 pounds each side on an ez-curl bar.
I note that Rippetoe recommends in his bench press video not to collar the bar when benching alone, so weight can be tilted off if caught with the bar on the chest.
So when should a barbell be collared?