Say, you'd been expecting a call and the person suddenly calls. Is there a word that feels more 'rushed' than pick up? I checked Thesaurus but none of the synonyms seems to fit the purpurse.
From en.wiktionary, snatch means “To grasp quickly. [eg] He snatched up the phone”. Related senses of this verb include:
• To attempt to seize something suddenly; to catch
• To grasp and remove quickly
• To do something quickly due to limited time available
• To take or seize hastily, abruptly, or without permission or ceremony
You can say that you grabbed the phone.
Merriam-Webster has the following definitions for grab:
to quickly take and hold (someone or something) with your hand or arms
to take or get (something) in a quick and informal way
to take or seize by or as if by a sudden motion or grasp
Similar to @jwpat7's "snatch", but with sillier overtones, there is snag:
snag (Infoplease): to grab; seize; "to snag the last piece of pie"
snag (Cambridge ACD): to obtain or catch something by acting quickly. "I hoped to snag a good job."
And, of course, ever since season four of the Simpsons, we've that lovely little word: "YOINK!"
You can use the verb scoop (up).
to pick up (something or someone) in one quick, continuous motion [MW]
He scooped the phone up. “Can't you people leave me alone for even a little while?” he shouted angrily.
[Needful Things: The Last Castle Rock Story By Stephen King]
Note: I admit that this is less common than to grab (the phone) but more precise for the meaning.