Cloud GPUs are not economical if you use them 24x7x365 (which for any serious deep learning researcher or engineer is usually the case). The only scenario I can think of in which they'd be more economical than something under your desk is when you need to run a massive and embarrassingly parallel workload. I.e. try training dozens of models at the same time with different hyperparameters, and run that for a few days. You could do it cheaper, but it would take a long time and it would be a massive pain in the ass, so you pay the pretty penny and get it done in a week.

For my needs I have a machine with a 2011-v3 socket, and four GTX1080 GPUs. Warms up my man cave pretty nicely in winter. I also have access to about a hundred GPUs (older Titans, Teslas, newer 1080s and Pascal Titans) at work that I share with others.

Now, regarding Titan. Titan is actually not that much faster than GTX1080, so in terms of raw speed there's no reason to pay twice as much. BUT, it has 4GB more RAM, which lets you run larger models. NVIDIA rightly decided that for a $100+/hr deep learning researcher $600 is not going to be that big of a deal, and priced the card accordingly. If your models fit into 8GB, you'll be better off buying two 1080's instead.

As to me, I'm thinking of replacing at least one of my 1080s with a Titan, to be able to train larger models.

On a purely TFLOP or even TFLOP/watt basis, it doesn't currently make sense to buy anything that doesn't run Pascal.