Here goes:
1.Papu in Crash Bandicoot (the original)
2.Gnasty Gnorc in Spyro (the original)
3.Ripto in Spyro (Ripto's rage or Gateway to Glimmer depending on your nationality)
4.Crush (possibly wrong name) in Spyro (Ripto's rage or Gateway to Glimmer depending on your nationality)
5.Gulp in Spyro (Ripto's rage or Gateway to Glimmer depending on your nationality)
1.Running around overheadish dodging enemy belly flops and spinning when enemy is lying on floor after attack. (in arena)
2. 3rd person chasing after enemy dodging obstacles and gaining on the enemy. (when closer to catching the enemy fires backwards) (on long path which loops to avoid running out of level if catching up takes a long time)
3. 3rd person flying around dodging blasts of fire and attracking also with fire (possibly could have to fly through rings to stay airborne as an adaptation?) (in arena)
4. 3rd person dodging charging enemy. bombs are dropped from above and when pickup must be thrown at the enemy to injure them. Enemy cannot stop after beginning to charge. (in arena)
5. 3rd person dodging enemy attacks similar to 4. however to injure enemy must run onto platforms making enemy follow. When enemy enters platform rocks fall from above onto enemy. Enemy constantly follows character instead of charging. (in arena)
Theres five that I remember off the top of my head that I love. (As you probably guessed I miss the days of PS1's or PSX's whichever you prefer.