I think that when we were all growing up most people just had more time to play Amiga games than they do now. But equally the genres, ideas and concepts were all new and exciting and most games were unique and quite original. These days most games are all from the mould of the genre they belong too, so although you may enjoy that type of game most of it's gameplay and style has been seen before.
But I personally still manage to find many games on all platforms that get me hooked.
The most recent was Lego Star Wars 2 on the PSP. I've been playing that in my breaks at work for a few months now. I completed the main missions but still keep replaying them all with different characters to try and find all of the secrets and unlock everything. I really did think that once the main game was completed I wouldn't bother going back but it is still as fun as you then get to do things in levels using the abilities of characters you didn't have access to the first time through.
Continuing the Star Wars theme, Knights of the Old Republic on the Xbox was another game that really got me hooked and from the moment I started playing I couldn't put it down until it was completed. That for me is still one of the greatest games created to date.
And there have been many more over the years on all platforms, especially RPGs on the PC and PS2.