Unbelievable game. When it says remake, it means it in every sense: new graphics and character design, re-recorded soundtrack, and some extra levels. Overall, as a big fan of Crash (I still have Crash 3 on the PS1), I didn't expect it to be **this** good when the game was announced, but I was thrilled when I played it. Almost everything is exactly as I remembered it, with clear improvements, and of course, I enjoyed it 100%. The only "negative" thing I found is that it might take some time to get used to the controls, because they are not exactly the same as on the PS1 (this is mainly for the depth, which may not be accurately represented in some levels, resulting in wrong moves), but after 2 hours, it's not a problem anymore.
P.S.: For an extra dose of nostalgia, try playing it with a controller, as the feeling is clearly better.
Edit: There are many people who say it's difficult (and indeed, the levels in Crash 1 are quite demanding), but I believe this also makes it quite interesting as it adds replay value. Personally, I would be disappointed if I bought a game for 30€ and finished it in one or two days