Is it possible to use standard tokens in a views field? I am using Drupal 7.38 and Views (7.x-3.11) to show fields. I can't seem to get standard token replacement working for text fields, e.g. [node:created] is not replaced with the relevant value.

This seems to work fine if I set views to show content rather than fields. Am I missing something obvious?
If you want to display the date the node was posted or created when showing fields, you don't need to use a token. Simply add the field Content: Post date to the fields of the view.

If you want to include this date in a Global: Custom text field in your View, be sure to have the field Content: Post date above the Global: Custom text field. The replacement pattern for the post date will appear by clicking on Replacement Patterns inside the custom text field (usually named [created]). You can also select Exclude from display in the post date field if you don't want it to show.

EDIT:
Re-read your question, and I guess you are using Token Filter to insert tokens like [node:created] in a Long text field in your node, right? If this is the case, I'm afraid Views will not do a token replacement when rendering the field. There may be a way to modify the Views formatter to do this, but that's beyond my skills. See this post for a similar situation - you are able to use token replacements in your Views Header or Footer custom text, but not in a Field.