It does take some investment to get going, but it slows down. It also depends on how you approach it, whether you get only what you need or feel compelled to try every other thing you come across.
I haven't kept a log on how much I've spend on vaping because for me it's about more enjoyment and less death. However, I would have spent about $4K on cigs after a year now and I know I haven't spent that much on vaping. Plus, I'm probably stocked for a year in DIY juice supplies and hardware. I pick up a few things here and there when I want to try something new, but only if it's something I really want to try.
I think the biggest savings comes with going DIY on your juice. If you're looking to save money, that's the best place to start.
The next place to save money is in atomizers and cartomizers. There's a few rebuild-able atomizer systems out there now which can reduce cost quite a bit. VaporKings is doing a bulk deal on atomizers that reduces cost a good amount and you can get cartomizers super cheap buying them in bulk from China.
Finally, going with a mod that uses replaceable cells reduces cost of ownership. With regular e-cigs like the eGo or Riva, you have to replace the battery unit when the cell wears out. The battery units have a high failure rate as well. It's more expensive than simply replacing inexpensive cells for a mod that will last damn near forever.