These are my notes on improving life on AA without status. It's a little long, and besides trying to improve your odds of a LFBU, it also addresses gaming your seat in coach to a better one, if you wind up stuck there.

If I've gone a little basic here, it's for future readers. The tips on how to get out of your less-than-optimal seat in coach, tend to go hand in hand with determining your chances on getting a LFBU; it doesn't improve your odds but while you're looking at that, you might as well try to improve your ticketed seat. I've never tried this for anything but domestic, 2 class so your results may vary internationally (which is where this thread started.) Finally, other carriers (Delta) have a Buy-F-at-the-gate product, so some of the notes here, may work there, appropriately modified.

Long before your flight:

Just so it's said, get an AA FF number. You'll need it to log in and change seats and online check in (OLCI). At the airport, you can check in at the kiosk with your AA number as well as your PNR.

ExpertFlyer (EF) will provide fare bucket detail for $9.95/mo or you can get a yearly subscription. A few-days demo is available for free. Other threads on FT discuss EF, you can search for those rather than have it all repeated here. AA's seat map http://www.aa.com/seatmap/viewSeatsSubmit.do is free. You can play with AA's seat map to get some of the information that EF provides, but it's not a substitute for EF. It is, however, free. If this is a one-time flight, free works. If you intend to be a road warrior, go and get the appropriate tools. (There are other products besides EF)

Since you don't have status, you need to spend extra time gaming your seats.

1) Set your [PDA] Calendar alarms for T-100h, T-48h, and T-24h. Check the seat map above using AA or EF. on AA, 'purple' seats in Y are elite reserved; You can check a few times prior to T-100, but odds are, you already got the best seat you can. Don't bother checking more than once a week or so. (T-100h refers to 100 hours before the flight time. Use flight local time, not your time zone, if you are working a flight that doesn't originate where you are. This is more important for itineraries with multiple segments.)

2) At the above times, or shortly thereafter, check for other seats in your cabin becoming available. As flyers with status move to better seats, or change plans, their slightly better seats in your cabin may be come available and you may want to snag them in case your upgrade does not clear. (Log into AA; select my reservations, click on the reservation and select different seats for your segments if it looks like you can improve.) While you are gaming a better seat in Y, check the other cabin to see how it's filling to give you an idea of your odds. EF is better at this, but AA's seat map is 'free'; if it tells you that the other cabins are already fully loaded no need to look at fare buckets in EF -- zero is zero.

3) T-24h and less seems to be the best time for improving your lot in life in your ticketed cabin. Normally you OLCI at T-24h or less -- hold off but keep checking -- every few minutes right after T-24h, then maybe every hour after that. You can keep changing seats before you actually OLCI. Better seats or situations may free up as people get upgraded, reschedule to other flights, etc. I've also seen the previously held 'purple' elite seats in coach become available here on less-than-full flights at T-24h. This seems to happens at T-24h on less than full flights, but I've seen it happen later or not at all on full flights. This is your chance to get out of that middle seat in back of coach to an aisle at the front of the cabin with a power port.

4) Get to the airport early at T-2h or a little earlier and make sure you find the kiosk. Checking in with a person equals NO shot at a LFBU. Most of the above is about getting a more decent seat and managing your expectations about getting a LFBU upgrade. Early is probably the best thing you can do to actually get out of your cabin if the odds are good. If first is full T-24h, sleep in. Once they've released seats to be LFBU seats, you want to be the one they offer the seats to, before they are offered to others and snagged. If you didn't have luck, here, you have your last chance for a better seat in coach via Express seats. Don't take the express seat offer when it pops up. Dismiss it. You'll get the LFBU offer at some point, and if you don't, when it shows you your seats, if you do a seat selection at that point, some seats will be marked with a price. You also get your last chance at selecting seats that are decent but free (i.e. row 10 in coach for free, vs 7 & 8 on a 737 which are $29 at the kisosk.)

I've still seen standby at the gate, after getting a LFBU but can't tell if these were all non-rev or others, including elite, who requested too late. So, T-2h is a key time.

Additional Notes:

[Domestic] LFBU gets you a better seat, includes your bag fees w/priority tag, on board meal when available and liquor when available. You get EQM and RDM from your ticketed fare. At this time, all fare classes seem eligible for LFBU (other airlines exclude some fare classes.)

If you have a multiple segment flight don't OLCI until T-24h of the later flight -- eastbound, this will be later than your 1st flight, corrected for time zone. (You may be able to make online seat adjustments after you OLCI or maybe not) If you are not offered a LFBU on later segments, and pass thru an airport with kiosks on the airside, you might be able to try again there -- haven't ever had the chance to try this.
If you get offered and take a LFBU on your 1st segment, and check bags, do so at the First (or Business as appropriate) counter -- they are tagged priority and shorter line.

Thus far, declining the offers of 2X or 3X miles at OLCI and the kiosk does not seem to effect getting offered LFBU at least not now. They will offer it in both places. (Discussed elsewhere and elsewhen on FT, these don't seem to be a great deal, compared to when AA sells miles on sale, unless you are already maxed on purchased miles. They sell approximately for 3 cpm.)

LFBU is a domestic product as of this posting. If you are XXX-YYY where YYY is out of country, your YYY return won't be in a higher class unless you get an op-up. On return, you may only be able to game your way to a better seat in your ticketed cabin. AA may change things at any time.

In another AA thread about upgrades, there was speculation as to catering having an impact on upgrade offerings. In 2 class, it's probably not an issue, but in 3 class, upgrades from Business to First may change catering requirements, so it may be in the airlines financial interest to limit upgrades from Coach to Business, and leave First empty. This may be something that overrides an empty seat map and attempts to predict upgrade odds.

I have no experience with multiple passengers on a single PNR. Splitting may improve the odds of one of you upgrading if one seat is available. Using a single observation which may be completely invalid, you may be able to upgrade 2 on a single PNR but wind up in separated seats, and try and do a seat shuffle once onboard. Decide if traveling together is more important than one traveling in the next cabin.

On aircraft seats, www.seatguru.com and others will help you figure out where to sit if you don't know the aircraft.

If you want to get an idea of AA will decide how to block the cabin on a particular aircraft, look at a AA seat map for a flight on a aircraft type you are interested in, that AA runs all the time, in the far future (4-9 months out); it will be mostly empty, and you'll get an idea of how AA is blocking seats -- you'll now have an idea of why you could only get a middle seat when you booked your flight on some aircraft. Finagling the class of service will get you an idea of if the flight is 2 or 3 class. Note: aircraft types do change seasonally, a flight using a large aircraft may drop to a smaller one during the slow season and ramp up vice versa.