Flight Load tools:

ual.com (free) - start booking a "standard" award for the city pairs and dates needed, and you will see the fare buckets which resemble something like this:

F9 C9 D0 Y9 B9 M5 H2 Q0 V0 W0 S0 T0 K0 L0 G0 A9 Z0 E0 U0

Note that you can only see up to 9 seats in each fare bucket so there could of course be many more available than what you see. However, this information is extremely useful, since, for example, if you are seeking an econ to biz upgrade and see the example above, this tells you that:

1. Economy is full-to-oversold, since they are only selling the expensive seats.
2. Business is filling quickly, since they no longer are selling the discounted biz class bucket (Z). Those 1k's holding biz class tickets are likely to get operationally upgraded to first at the gate.
3. First Class is likely wide open, as they are still selling the "A" inventory.

Please refer to ozstamp's excellent primer on these buckets here

If you are looking for an econ to biz upgrade then you should hope that there is a lot of availability in F C D A and Z. If you are looking for a biz to first upgrade then you hope for a lot of availiability in F and A.

You can also try looking at award seat availability at ual.com but it is really hit-or-miss to see anything unless the dates are far in advance. Begin by booking a "saver" award ticket for the dates and city pairs. If you are lucky you will see the following info:
R = XF = First Class
X = NF = First Class Upgrade from Business
O = XC = Business Class
I = NC = Business Class upgrade from Economy
N = XY = Economy Class

So if you first don't see this (in other words, you get the message that no flights are availiable), go back and try the pull-down menu for not only economy but business and first class as well, since on any given flight they may have R and/or O available when N is not being offered for award travel.

ExpertFlyer.com ($10/month):
Provides seat bucket availability for every airline under the sun. You can also look +- 3 days from your date of travel, so you can see a full week of availability in one query as well as save queries too. An absolutely fabulous tool which I credit for finding 4 operational upgrades this year for me already. In fact, since subscribing I have had 2 r/t to Asia all operationally upgraded. If I continue to be a little flexible on the dates and routings I hope to have a few SWUs left over at the end of the year. ^

Seatmap Tools:
As per the previous post, you can get underway in booking a fake first or biz class reservation on ual.com and toward the final end of the process you can look at a seat map. However, this is a really hassle to do. You might wish to use orbitz.com for a fake booking, as you can see the real-time seat map after the first query submission.

Then again, subscribing to ExpertFlyer provides seatmaps too, and you can save queries, etc.

@:-) Please note that just because the seatmap shows all kinds of availability does not necessarily mean the cabin is empty! There are often many confirmed seats which simply have not been assigned yet (this is especially true for premium cabins, as most flyers consider all of the seats to be fine and will just pick what is left when they check in at the counter) @:-)

Wait List Info:
Naturally, the last and most important bit of into to get is the number of people on the waitlist. This can only be had by calling reservations. I have found the 1k desk people to be very forthcoming with this, but my friends without status usually get the brush-off on this topic.

Good luck!