Ninja Ryuukenden III: Yomi no Hakobune

At the title screen, let it fade out to the intro and press Start to go back to the title screen again, repeat this 6 more times (you should have seen the title screen a total of 8 times), at the 8th title screen, press and hold Up, Left, A, B & Select and press Start. If done right, you'll have 99 continues.

M - Medicine potion, P - Power-up, R - Ryu, S - Shuriken

Japan version only

In Stage 6-2B, grab the 1-up, backtrack to 6-2A, then return to 6-2B. The 1-up will have reappeared, along with all other power-ups in the room. You can repeat this process until the timer runs out.

In Stage 7-2D, grab the 1-up, backtrack to 7-2C, then return to 7-2D. The 1-up will have reappeared, including all other power-ups in the room. Again, this can be done repeatedly until the timer runs out.