I have had recurring nightmares of my bike coming loose from the trailer and bouncing down the road- that would be an unfortunate event that could bring a grown man to tears. I haven't been thrilled with the quality of what I've seen in LOS, so I ordered some stuff from the States.
I think two sets of straps (in conjunction with some sort of front wheel chock/lock) are necessary at a minimum, and as I might be occasionally trailering two bikes, I got four sets.
I couldn't decide between the current 'best', which probably are the popular 69" cam straps from Ancra (ratchet straps aren't used much for bikes anymore as it's too easy to over-tighten them and damage the bars or fork seals- cams are also smoother and easier to use one-handed or when you're by yourself) along with a set of soft extensions, or a set of newer-on-the-market Lockstraps, which have the advantage of locking carabiners an an attached soft end (both have been shown to have very little 'creep', which is loosening over time under stress- the Lockstraps also have a cable running through them and are a bitch to cut without proper tools).
Ancra tie-downs:
+
Lockstraps:
I also ordered a second-generation Canyon Dancer (which puts way less stress on the bars than the previous model due to the addition of plastic cups on the ends):
I also grabbed a Lockstraps helmet lock, which can secure a helmet and/or jacket:
As always, I would be interested to hear which other products/methods anyone else uses.