It makes a decent difference in games when loading maps (mostly map transitions like aigomorla said above). And maybe overall desktop Windows 'responsiveness' is a bit snappier for some applications.
Some open world games benefit from SSDs a bit depending on how they load in the assets as you move around. In Skyrim I found that it virtually eliminated all stutter related to assets loading in from the 'grid' pattern that the engine loads assets into (it's like a 6x6 square grid and you're in the center, as you move around things pop in at the edges of that grid; it accelerates the loading of that stuff a bit). Although it's not a major difference (modern HDDs load stuff in Skyrim already fast enough, but sometimes you can get occasional stutter as the environment loads around; then again we're talking about Skyrim and the GameBryo engine here, it's archaic). It's more of a 'quality of life' improvement in those cases than a significant speed increase in loading the environment as you move.
I only have a basic SSD though, from Crucial MX series I believe. It's for office stuff, not much storage space at 250GB. I only tested a few games one by one including Skyrim, Mass Effect 2, Dragon Age Inquisition and the most recent one being Monster Hunter World. The most noticeable difference in speed was essentially loading maps (Monster Hunter World was the one where I noticed the best difference, loading the maps was significantly faster in that one, whereas the others the difference wasn't as good since they were older games and modern HDDs do the work just fine for those), or maybe loading the game itself (which is not that much anyway). The difference in speed for loading maps is pretty good I must say. I haven't done any analysis, just observation based on what I was "used to" with those games and my estimation is maybe a 50% speed increase? Maybe? At least in Monster Hunter World it felt that much faster to me. Then again don't take the number for reference, it's just an estimation.
With this said, I stick to my two HDDs for my main system for now (and been like this for years). The storage space-to-price ratio on HDDs is still the overall winner in my opinion today. At least when it comes to 2TB+ in storage space necessities. I for one need around 4.5TB so that's why. The price for 1TB SSDs did improve a lot in the past year or so (many have reached nearly equal prices to 1TB HDDs). However, getting to 2TB+ on SSDs hurt the wallet more than it should in my book, and going 4TB+ is currently just absurd. The last time I checked around December last year for one 4TB SSD on Amazon would have been around $870; Canadian dollars. By comparison you can get something like a single 6TB Western Digital Black HDD and be set for your next 10 years worth of games storage requirements and it'll cost you just about $300.
Ironically enough I wouldn't recommend SSDs for their 'speed' compared to HDDs. I'd simply recommend them because they're the new 'standard' of storage on PC and consoles alike now. In coming years the only new tech and improvements to storage drives on either side (PC or consoles) will happen on the SSD field, not HDD. I don't think we'll ever hear of new HDD tech ever again. So right now I'd say stick with HDDs if you need a lot of space (around 4TB+), but get an SSD if you're fine with 1TB or less, regardless of speed differences. Because at or below 1TB the prices are nearly identical and when you're at that point you might as well just get an SSD really.