Case Clinic is a peer-coaching method from Theory U. It has a practical output (helping someone with a challenge they're currently facing), and it tends to produce a lot of insight and interpersonal bonding. It's an excellent place to start, you can get a long way in one meeting.
Feelz Circle: 3 processes for sharing emotional care between friends/ comrades/ lovers.
The Circle of Trust approach from Parker Palmer and the Center for Courage and Renewal. Includes some guidance for cultivating a safe space for vulnerable conversations, plus great descriptions of why this is valuable.
Mia Mingus wrote this excellent guide to Pods and Pod Mapping for the Bay Area Transformative Justice Collective. In this context, your pod is "the people that you would call on if violence, harm or abuse happened to you; or the people that you would call on if you wanted support in taking accountability for violence, harm or abuse that you’ve done"
Metagame Mastermind: a kind of stoic crew. 3 people, 3 week sprints, 3 commitments (one life practice (e.g. meditate daily), one renouncement (e.g. no sugar), one gift to the world).
The Elephants long term personal development for Crews, focussed on goal-setting and accountability.
RMMAN Pods Guide - beautifully documented guides to starting different kinds of support pods, from the Rocky Mountain Mutual Aid Network.
Working Out Loud: a guided 12-week process for peer support in small groups, suitable for workplaces: what am I trying to do? who is related to that goal? how can I contribute to them to deepen our relationship?
Be The Change Earth Alliance use Action Circles to support people who want to change their life to be more ecologically sustainable. They have a comprehensive best practice guide for convening these circles, including sample agendas, facilitation and communication tips, etc.
The Scuttlebutt software community are actively forming crews they call Faerie Rings. Documentation currently focusses on how to do matchmaking to form crews within a congregation. Faerie Rings are mostly "get to know you" spaces for people who are participating in a big distributed project, but don't have many opportunities to connect face to face.
Ako Groups: peer support within a learning context, e.g. university