Although I know a little less about these than the "big Four", I've worked a bunch with them, and both my brother and I owned a pair for a long time. (We used to roadrace each other on 'em for fun!)
The 500 was Honda's reply to folks who were "inseam challenged" and those who did not care about raw power, but more civility in their rides. As such, it was Honda's crowning achievment in smoothness, their best before the Gold Wing series.
The quiet and smoothness came at a price in performance, though, and in handling. The quiet mufflers, surprisingly so for their short length, were restrictive to get that silence. Opening up the exhaust a little has big paybacks, but will require rejetting. The airbox was likewise restrictive, and opening up the inlet holes will solve that without buzzing your ears with intake noise. Use a K&N air filter, the one that replaces the stock unit in place, for the best performance with the least annoying noise. Then, either rejet or run D8E sparkplugs afterward.
The inlet tubes were not made for flow, but for easy production and maintenance. You may even find large mismatches in the bores, and the screws that are used for carb balancing often stuck into the passage about 1/8" or more. If you're looking for upper-end HP, match up the intakes tracts and trim those screws. Remove the rough casting marks inside the inlet tubes, too. You can actually pick up almost 10% more flow with these little things.
If you're tired of grabbing 2 handfuls of throttle to get from 0-70 MPH, try this: get and install aftermarket throttle cables, which are thinner than Honda's (but won't have that nice nylon slider coating). Then, inside the throttle grip, lay some small diameter wire in the groove where the cables run in the twistgrip: this makes a slightly larger diameter circle in the grip. Don't make it so big a wire that the thinner throttle cables won't ride in the grooves. (Alternatively, you can get a fast throttle grip, but you'll sacrifice the handy switches in the process.) Test it to make sure it glides smoothly, then reassemble.
The springs on the stock 500/550 were very soft, too soft for spirited riding, and they sagged quickly. Get 100 lb springs for the rear when you replace the shocks, and shim the front springs inside the fork tubes with at least 3 washers of the diameter that fits the tubes inside. Then add air valves to the caps to make air forks out of them: run 10 PSI without a fairing, 15 or so with a fairing.
The 500 frames usually ran straight and true, even to 110 MPH. They really like TT100 tires, if you don't carry touring loads. The Continental motorcycle tires match the lean angle of the stock 500/550 perfectly and make a real good all-around tire for these bikes, lasting a long time and gripping well in the wet (and ice!).
The swingarm bushings and steering head bearings were just like the "big four" and suffer the same maladies. Fix them the same way as the CB750K series bikes. And. if you have over 10,000 miles on the wheel bearings (original Honda), they're gone. Replace them with Timken or Bower bearings for a much more responsive and confident ride.
Hop-ups: Add 4 teeth to the rear sprocket and get a cam. Don't get high lift, get longer duration - BUT: not a LOT more duration, because it is a small-bore engine. A little goes a long way. Adding 5 degrees of overlap and 10 degrees of duration should be your limit for non-racing driving: it will REALLY wake up the "mid-four". Don't bother with bigger carbs: port it in the head instead. The stock carbs can make a lot more HP than they do: make a "pocket" above the intake valve, then raise the exhaust ports about 2-3 mm and smooth 'em out. This will add up to 10 HP to this neat engine, which is a lot.
In response to a question about pod/stacks and 4-1 exhausts:
I dislike open airboxes for noise reasons. Unless they are fitted with velocity stacks, the improvement is usually overrun by the annoyance, with maybe a 5% change. You can get almost 5% with just matching the ports. 4-into-1: I have never seen them make any difference. 4-into-2: these make quite a difference on the 500/550, if you can get good ones. Unfortunately, the good ones also block the oil filter....
On a 500/550, for about the same $$$ as buying 4 K&N filters with velocity stacks, buying 4-into-something pipes and fighting with the resulting tuning, you can get a cam with more overlap and install it, right in the frame. For performance, that's the first place I'd go with the 500/550. Don't get more lift, just longer duration (this will cause more overlap, by design), maybe 8-10 degrees. This can add 10 HP to the under-aired 500. I don't know if Yosh still makes the street cam, but look around - maybe someone has one. Update 2020: use the 126-00 from Megacycle, good all-around and increased power.