To join a conversation or situation in which one is not welcome or invited; to interject (connotes a rude or discourteous interruption).
To join a queue not at the end, but in the middle.
To interrupt a conversation by introducing a different subject or making a comment.
To intervene in a dispute, or in a conversation.
To insert something (or oneself) between other things.
To be inserted between parts or things; to come between.
To offer (one's help or services).