You can dye your hair to various shades without bleaching if your natural hair color is relatively light or medium-light. Here are some examples:

1. Dark Brown to Medium Brown: If you have dark brown hair and want to go a shade or two lighter to a medium brown, you can often achieve this without bleaching. Darker hair dyes can cover lighter hair and provide subtle changes in tone.
2. Warm Tones: Switching between warm shades like reds, coppers, and auburns is usually achievable without bleaching. Darker red shades can be applied directly to brown hair, while lighter reds might work on lighter brown or darker blonde hair.
3. Temporary Colors: Temporary hair dyes or color-depositing conditioners can add pops of color like pastel pink, purple, or blue to light brown or blonde hair without the need for bleach. These colors typically wash out after several shampoos.
4. Black to Darker Shades: Going from black to a slightly darker shade, such as a very dark brown, may not require bleaching either.
5. Gray Coverage: Coloring gray hair to match the original hair color or to darken it can be done without bleaching.
6. Highlights: If you want to add subtle highlights, using a highlighting kit designed for no-bleach or low-lift situations can give you a bit of dimension without dramatically altering your base color.

However, to achieve significantly lighter shades or vibrant colors like platinum blonde, pastel hues, or rainbow colors, you will almost always need to bleach your hair to remove the natural pigments and create a blank canvas for the new color to show up properly.

Keep in mind that the effectiveness of dyeing without bleaching also depends on the quality of the hair dye, the current condition of your hair, and the contrast between your natural color and the target color. Always do a strand test before coloring your whole head to ensure the results meet your expectations.