You could cut up your tights to give them a distressed look and build a grunge outfit around them; however this will probably mean that you will get one wear out of them before they become shredded beyond repair!
A less destructive way to make your tights totally unique to you is to dye them. Instead of just dying them a plain all over colour, why not experiment with different patterns and textures?
You could ombre your tights by choosing a coloured pair of tights and dip dyeing them either a lighter or darker colour. It is best to use a heat up hand washing dye for this so you can control how much of the tights you dye. You’ll want to start just above halfway down the tights and soak them in the dye. Do this for about half the recommended time on the package then remove half the dyed area from the pot and continue soaking only the very bottom of the tights. This is what will give the fading ombre look.
You can also tie dye your tights using a similar method. Scrunch your tights up into a ball and tie them with plenty of elastic bands in all different positions (you could use string but elastic bands will work much better) then use hand washing dye or microwave dye and follow the instructions on the packet to get the timing right (different brands of dye will have different instructions.)
Make sure you rinse out the dye with the elastic bands still on and do not remove them until your tights are totally dry to avoid ruining your pattern. There is no real way to get an exact pattern with tie dye so your tights are sure to be unique (no matter how many pairs you dye!)
You could dye each leg of your tights a different colour if you fancied being really adventurous!
You could print patterns onto your tights using waterproof paint (fabric paint is best) with sponges and card/ plastic stencils. Hearts or flowers are a good place to start as you could easily make your own templates (you could even print some off the internet.)
Printing words on your tights is trickier but with a little practice you can spell out anything you want. This is particularly effective on sheer nude tights or opaque white tights to really make the letters stand out.