Some airdrops are very good if you can get in on time. A buddy of mine gets deep onion airdrops every week. You get free coins. So, definitely profitable. You just need to spend some time on bitcointalk.
I've yet to get a true 'out of nothing' airdrop that meant anything... supply and demand. Airdrops lead to tons of supply and little demand since everyone got some. But... yes my
DeepOnion signature* campaign airdrop has been massive. I haven't sold anything yet but as of this writing, if I were to cash out I could sell my DeepOnion for $37,000. In fact, it's the single most valuable hold now, just ahead of Bitcoin. I'm not cashing out because I believe DeepOnion will go much higher than $3 when the roadmap is complete.
*what I mean by signature is that the airdrop campaign started off with a BCT posting requirement, but has shifted slightly away from that.