My all round must have is the Boots Botanics 97% Organic Hot Cloth Cleansing Balm from the high street.
I know I've mentioned this balm before, but it's a really effective makeup remover, has good slip for facial massage and a great price point - it's one of the only really good cleansing balms I've tried only BD6 (if you've used any others, I'd love to know which ones you rate - tell me in the comments). It has a luxe, buttery texture and a formula rich in shea butter, rosehip, sweet almond and jojoba oils, good for all skin types. I find it can leave a little bit of moisture film on skin after rinsing, so if you're oily or combo you might want to follow up with a face wash or sweep of micellar water/rose water afterwards.
As a cleansing fanatic I believe it's essential for clear and radiant skin, I have a lot of cleansers in my arsenal, and will reach for different textures depending on how much time I have and how much makeup I need to remove. Balms are one of my favourite cleansing textures for days when I'm wearing more makeup than usual, as they help to emulsify and dissolve it all away quickly (although I sometimes use a separate eye makeup remover first). I also like to use them when I have time to do a facial massage, in which case I'll do one cleanse with the balm to remove makeup, then apply again for massage. Balms are great for this as they stay slippy on the skin whilst also giving slight grip, so you can gently stimulate your skin without pulling or dragging. They're also easy to use (massage onto dry skin, add a little water to emulsify and remove with a damp cloth - which gently exfoliates, too) and work really well on most skin types as they cleanse and nourish without stripping skin.