First and most important: stay away from the dealer-recommended OEM replacements. The Dunlop F11/K627 Qualifier combo was a middle-of-the-road tire 25 years ago. They were seen as a performance limiting factor when our bikes were new by nearly all magazine testers. The fact that Honda dealers still recommend them when you walk in and request a tire for your bike borders on criminal negligence. They are simply dangerous as far as I am concerned. They corner poorly, ride like they're made of wood, break loose under power with little warning, and are slick as banana peels in the rain. They also wear poorly and they're relatively expensive. I can't imagine a worse tire. Yet Dunlop continues to make them and recommend them.
One step up the ladder are the bargain replacements: Kenda, Cheng Shin, IRC and the like. These have gotten better, but the technology is still from 20 years ago. You gets what you pays for.
Next up, long life tires. The Dunlop K491 is a popular choice, but numerous listers who do long distances have had unpleasant incidents with them in the wet. They have a less-than-round profile as well, and unless you ride where you *never* encounter curves or traffic that might make you perform emergency handling maneuvers, you will find lots of shortcomings in these tires. These are sized in the quaint old alphanumeric American tire sizes, like MR90-18 and the like.
There are a whole slew of stock-size bias ply tires made by leading mfrs like Metzeler, Dunlop, Bridgestone, Avon, Michelin, Pirelli, and Continental. I list these in the order of my personal preference, and I've tried some of each except for Pirelli. Something to keep in mind is that tire compounds have evolved enormously in the past ten years especially in regard to silica compounding, so a newer model tire is going to have a real performance/handling/lifespan advantage over an older one. For instance, the Bridgestone Spitfires (one of the most popular budget tires among listmembers) or a Metzeler ME33 is not going to have as modern a compound as, say, a Metzeler ME330. Cheaper tires have lower-spec carcasses, which make for a wide range of handling responses. There is a certain wisdom in 'you get what you pay for' in this segment. Some are notably better than others. I tried a set of Avon Roadrunners. They lasted too long; I was glad to get them off the bike. Hard cornering turned them blue and the rubber balled up on the edges like on race tires. For other styles of riding, they may be fine. It's hard to go wrong with Metzelers. And as Joey mentioned, the Bridgestone BT45 is about as good as you can do in this segment. Stable, predictable, handle well, decent in the wet, better than so-so treadwear.
The Metzeler ME880 is sort of in a class of its own here, because they're very good on treadwear but have up to date compounding so they can be made to handle. You won't mistake them for radials, but they're (IMO, and I've been through several sets) the best compromise on these factors you can make. Fine in the rain too. I just got another set for the Couch Rocket.
Then there's radials. A little history here first. In the infancy of the list some ten years ago, Tony Donisi first advocated the use of radial tires from testing on his V65 Magna. Trouble was, radials have never been made in 90 series tires, which all Sabmags are spec'ed for. You have to use 80-series tires. The big Magna uses 110/90-18 front, 140/90-16 rear tires. Tony's solution was to use a 110/80ZR18 front and 150-80ZR16 rear, using Avon ST23 radials. (The V45, VF700, and V65 Sabres use the same front tire but use a 140/80ZR17 rear rather than a 130/90-17 bias ply.) Others tried them on Tony's recommendations and the response was nearly unanimous in favor.
There were some dissenting voices, though, and that's because they are not a panacea to cure all the handling ills that are designed into our bikes. One issue is an increase in speedometer error. You can expect about 10 percent, and somewhat less with odometer error I have no idea why or how this could be. Go figure. More of an issue is the range of handling characteristics. The difference in bias-ply and radial casings is huge. The smaller diameter of the tire does a couple of different things to/for the handling. Since both the V65s use a leading-axle fork design, trail (measured as the distance between two points on the pavement, a vertical line through the front wheel axle and and the steering head's extended center line; literally the distance the contact patch trails the steering axis) is decreased when wheel diameter decreases. This decreases straight-ahead stability and quickens steering response markedly. If you value sharp handling, this is a *real* plus. If you like droning on the interstate, it's not so good, because you will have to put a little more effort into keeping it tracking straight. More correction is required. This becomes automatic after a while, but it takes a little getting used to. But otherwise it's like you just installed power steering. Big bikes just shouldn't be as quick at transitional response as a sabmag with radials is. You can really surprise your sportbike buddies or, better yet, unsuspecting squids. In fact, squid hunting becomes considerably less sporting. The rear tire is slightly wider but the same diameter. There are no clearance issues.
For me it's well worth the tradeoff. With radials you get the most modern tire compounds, which stick like glue, stop on a dime, and shrug off water. You get decent tread wear, better than the OEM tires by far, and really it's only limited by your riding style. You roll over rocks rather than skitter over them. You can carve twisties in the rain, no problem. You can confidently handle the bike down to the peg feelers, and look for ways to keep parts from dragging. You break loose very progressively, so progressively that you learn how to control it. Simply put, radials allow you to use more of the bike's performance. Most people report a night and day difference in handling, as well as taking some time to get used to the way the bike wants to dive into turns. Again, after a while compensating for this becomes automatic. It also feels like the bike lost about a hundred pounds. This is a rare effect to achieve with ANY modification. Well worth it just for this.
The Dunlop D205 was the recommended radial tire for many years, and they still are, even though they're a harder to find since most sizes (but not ours) were superseded by the D220. They are stiff at the sidewalls, which makes for rail-steady handling when they are leaned over. They like to "take a set" and you can tell this because when they are worn they are characteristically beveled. This is also because of a somewhat triangular profile. For a while the only alternative was a set of Metzeler MEZ-1/MEZ-2s, which had a somewhat more rounded profile. This made for somewhat more progressive turn-in at the expense of that rock-steady line through curves. They also didn't wear as well and the rears tended to flatten in the center rather quickly. The Avon Azaro II (AV35/AV36) were introduced not long after, maybe about 1997. They were pretty similar to the Metzelers in profile and performance, but cheaper.
About three or four years ago Avon replaced the AV35/AV36 Azaro II with the AV45/AV46 Azaro ST. This was a totally different tire, and a huge improvement. It had a more triangular profile (like the D205) but softer sidewalls. They'd take a set in curves, but were somewhat more progressive in turn-in and more willing to change line while leaned over. A real bonus, for those folks who change their own tires, is that they practically install themselves. They are not nearly the effort to wrestle on and off the rims that the D205s are, which for some people is reason enough to switch. And as an added bonus, they last a little longer. These are my current favorite. I have a set of worn-out D205s on the Second Sabre, and hopefully I'll be putting on a set of the Avons next. I've been through innumerable sets of the Dunlops--I mean, like 30 or 40 total--and four or five sets of the Azaros. You really can't go wrong with either. If someone else mounts your tires, I'd call it a wash. If you do your own, you'd really rather have the Avons. They're the current state of the art.
My personal riding philosophy favors having the tire that gives me the best advantage if I get into an unpredicted situation, whether it's an evasive maneuver or a maximum braking exercise. I enjoy a sharp-handling bike as well. Still, since I live in a flatter part of the Midwest than I used to, I can see some advantage in a tire I don't have to replace every 4000-6000 miles. That's why I have ME880s on one bike and D205s on the other.
So, if you're looking for reasons to stay with the spec-size bias-ply tires or experiment with radials, I hope that the above will help you identify some factors that will help you decide which way to go.
Note: Some Azaro sizes have been discontinued. The Avon Storm replaces those discontinued tires.