'Perfect Beautiful Good' by OnYourMark - there's just something about the thrill of the chase that spills over into Peter and Elizabeth's lovelife, so Neal has no idea how much Elizabeth would like to thank him for... Peter/Elizabeth/Neal.
'These are the words I never said (this is the fear)' by elrhiarhodan - in the aftermath of the tracking anklet coming off, Neal tries to figure out what it is he wants and what he might never get to have. Peter/Neal, Elizabeth/Peter.
'No, and Here's a Dozen Reasons Why' by china_shop - running alongside seasons 1 and 2, I particularly liked the way it starts with Peter telling his agents how to avoid letting Neal scam them and develops as the relationships within the show develop and deepen. Peter/Elizabeth/Neal.
'Full Immunity' by OnYourMark - now Peter has put his FBI badge on one side so Neal can be completely honest about what he's done in the past without fear of prosecution, here's a bunch of other occasions when the two of them (and El, of course!) have done just that. Peter/Elizabeth/Neal.
'Both Sides of the Conversation' by OnYourMark - an AU where rookie FBI agent Peter Burke is called to investigate a robbery in an art gallery and runs into a situation that is far beyond his ability to control. Hijinks ensue, with Elizabeth and Neal at their heart. Peter/Elizabeth/Neal.
'I Lie, I Cheat, I Steal (and I Just Don't Get Any Respect)' by fiercelydreamed - a nice crossover between two of my current favourite shows, where Nate decides that what they really need for their next con is a particular con artist, one who's currently working with the FBI. Various pairings implied.
'Somewhere I Have Never Traveled' by Sam Storyteller - riffing off the season 2 episode 'Company Man', this excellent story asks what if Peter Burke had gone corporate instead of joining the FBI and how might he and Neal have crossed paths after all? Peter/Neal.
'A Mile Away and Wearing Your Shoes' by BlackEyedGirl - in which Neal and Peter find a magical artifact in an FBI bust and end up experiencing the view from the other side of the desk. Yes, it's a bodyswap story, just go with it! Peter/Elizabeth/Neal.
'love is not a battlefield (i am no hercules)' by hoosierbitch - I've often struggled with rape-recovery stories, mostly because too many of them stress the power of the healing magic cock, but for beautifully-written stuff like this I'll make an exception. Flashbacks for Neal, realistic reactions from Elizabeth and Peter. Peter/Elizabeth/Neal (eventually).
'Always Starts the Same, With a Boy and a Girl' by lightgetsin - first of a bunch of recs from a new fandom, as I've become utterly smitten with White Collar and its OT3. In this AU story, the author wonders just what might have happened if Neal had met El first, instead of Peter and works on from there. Peter/Elizabeth/Neal (eventually).