Sticking with diatonic harmony, the most common examples are going to be scales that outline some extended harmony because there can be multiple altered chord factors which are either nonsensical or impossible to spell without a sharp and flat due to their function relative to the key. Pick up any Aebersold book and head to the scale syllabus and you'll find some examples.
Lydian dominant is a nice self-explanatory one - contains a ♯4 and ♭7. Diminished scales are also frequently impossible to write without a sharp and flat. Say we're in Cmin and want to play a diminished scale over the ii. ii°7 is D-F-A♭-B♮. Something needs to give in order to fill in the gaps without an augmented unison, so this scale will contain a C♯ as the 7th step in order to have an interval of a second between each step while still outlining the correct diatonic chord. Both half-whole and whole-half variants suffer this.
It's worth noting most of the Jazz scales commonly named after modes aren't necessarily used in a "modal" way. For instance the function of the aforementioned lydian dominant would be more likely found played over a V+11 than to actually emphasize the mode itself. The scales just share some common characteristics and inherit the name. Super-locrian is a notorious example that has almost nothing to do with the locrian mode other than it's underlying interval pattern.