Depends on the game. Most single player games won't see much increase over a newer platter drive if the game has any optimization for buffering the data needed ahead.
Where SSDs shine is in MMORPGs. When you have a screen full of 20+ avatars and each avatar has 7-10 different textures to display, theres a TON of info that has to be fed to the GPU. There's no way to pre-buffer that quantity of data so a HDD has to spin, find the info, and then feed it to the GPU. The SSD can access the info much faster and there's not waiting for the platter to spin to the next texture to load.
A faster hard drive or SSD will simply mean faster level loads. It used to make a bit of a difference but drives are fast enough and the game software good enough that buffering is very good.
There are games that don't buffer as well and loading is too frequent.
Ideally, a game will load everything you need into RAM for that level as well as the next level, then when you enter the next level (seamlessly) it gets rid of the last level and buffers the next. This doesn't happen often but it's getting better.