It can be used in both the present and past tense:
* Present tense: I encounter many challenges in my work.
* Past tense: I encountered a bear on my hike.
Other verbs with similar meanings include:
* Meet: I met my friend for coffee.
* Come across: I came across a beautiful painting in the museum.
* Run into: I ran into my old neighbor at the grocery store.
* Bump into: I bumped into my boss at the coffee shop.
* Cross paths with: We crossed paths with a group of tourists.