This is another unanswerable question regarding which my research activities consisted of thinking about it while riding. And I think we've sampled this subject on occasion. But I think it's worth looking closer at why you don't hear of many doping cases arising out of the classics. Should we conclude that they aren't as compromised?
First, a little perspective. We should talk about the last 10-20 years, which itself can be broken up into distinct segments. Prior to the 80s, the drug of choice was amphetamines and other short-term stimuli, so of course the classics were like any other race. Not sure what to say about the 80s, really. But by 1992 EPO had changed the game, and here's where it becomes worthy of discussion.
Next, some factual background. I am going off the list of doping cases from Wikipedia. I can't say whether this is the definitive list or not, so feel free to dispute this. Anyway, there are a number of continuous doping confessions -- Jesper Skibby and PDM generally; Bo Hamburger (La Fleche winner); T-Mobile (including Zabel); Jef d'Hont; Pot Belge; etc. -- which obviously implicate some classics performances, and there have been a handful of busts at classics races, including Fuyu Li's clen issue from Dwars Door Vlaanderen earlier this year. But the vast majority of cases have arisen in grand tours. That's just a fact. And from that fact there are two possible conclusions:
- Riders in the classics are cleaner; or
- Testing around the classics isn't as effective.
Let's start with #2. Why wouldn't the testing around the classics be as effective?
The Organizations: Ownership of the classics is largely covered between ASO, RCS and Flanders Classics. I can think of a few exceptions, like the Giro dell'Emilia and E3 Prijs, but this mostly covers things. Obviously ASO isn't to be trifled with, and RCS is pretty sophisticated. I don't know as much about Flanders Classics, but I do know that the winner is whisked away by the UCI for testing, so at a minimum Flanders Classics has the UCI handing things. How many other tests do they conduct? Not sure, but they nabbed Fuyu Li at Dwars for Clen, so it's more than trivial. So I don't see this as a likely difference from the grand tours.
The Cultures: I raise this because, for at least one month a year, cycling culture is truly distinct from the rest of the season. The Classics are a world unto themselves. So if those Classics aren't producing many positives, could it be that Belgians are less sensitive to doping? One reason it's tempting to ponder this kind of gross generalization, is the Pot Belge case. Johan Museeuw is one of the country's biggest stars ever, and confessed in retirement to participating in the ring of cyclists who were stupid enough to take a mix of coke, heroin and other stimuli. But he took four years to confess, during which he kept his job with Quick Step. Museeuw also remains a commentator for Sporza (and presumably stars as the voice of Groundskeeper Willie in the Dutch issue of the Simpsons), and has a line of carbon frames out. His punishment in the criminal case was 2500 EUR, about the cost of one of his frames.
But is this a cultural distinction, or is it merely consistent with the worldwide tendency to treat our biggest stars differently? Neither Lance nor Landis has spent any time in jail for their alleged misdeeds. So, you know, glass houses. And Belgian Cycling bounced Dave Bruylandts shortly after his podium in the 2004 Ronde (though his tactics alone were sanctionable...). Anyway, I don't see enough to justify a claim here, so let's move on.
The Logistics: Everyone tests the winner, but the real threat is in random testing. During the grand tours you have the entire peloton under your control for three weeks. How many non-winners can you nab during a one-day race? Some apparently, and the fact that the UCI is doing the testing means that their out-of-competition testing is as much a deterrent as in-race randoms during the Tour.
So the lack of testing isn't a very likely candidate, though there are almost certainly differences of degree, particularly versus the Tour who have employed AFLD to increase the number of controls, so maybe there's something here. But it's not clear to me.  Actually I would say that the number of guys tested at the grand tours is definitely higher. There are the testers themselves, working a bit harder in July than the rest of the year (to say the least). And there are multiple winners (stage and GC) tested every day for three weeks. That's a difference.
So #1: Are Classics riders cleaner?
I can think of a few reasons why this might be so.
1. Day to day recovery isn't relevant.
One of the primary benefits of EPO and testosterone and the like is the ability to prevent you from experiencing the dreaded jour sans. Off-days in the classics happen too -- you can get sick or just not have it for some reason. But the most common threats to day-to-day performance -- exhaustion from the previous day's or days' effort -- is nonexistent. So to the extent you might need PEDs to guarantee consistent performances, it's not as much of a concern in the Classics. I am not dismissing the temptation out of hand; Classics riders have full seasons to concern themselves with. But it's not the same.
2. The money isn't as big.
While this speaks quite poorly of humanity in general, the fact is that the Classics don't have the same importance in the grand scheme of things as the Tour. Sponsors don't count on a strong Paris-Roubaix the way they do count on getting noticed in July. A run at a stage of the Tour is in effect the equivalent of one or many 30-second TV spots broadcast to 181 countries simultaneously. This alone justifies a lot of sponsors' investments. The Giro and Vuelta have a regional version of this appeal. The Classics -- they're watched and beloved, but not on the same scale.
Consequently, the pressure to perform at the Tour is also on another level. The need to do well over three weeks is clear. Also, the existence of numerous prizes every day brings several other riders into the fold, in search of a result of one kind or another. In the Classics, if there are secondary prizes, they are almost universally ignored.
3. Taken Together...
So, there are more performance-related reasons to dope at the Tour. And there's more money around for doing well. So the expense of doping is more justifiable. Assuming riders live according to the most basic cost-benefit principles, if for the Classics you decrease the benefit (performance) and hold the cost ($, enforcement) steady, that alone would decrease the likelihood of doping. If the economics are as I suspect, the Tour riders have both more benefit and less cost, a double-whammy of increased incentive to cheat, as compared to their one-day brethren.
This is an intriguing distinction, going forward. The current environment is pretty hostile to doping and the testing regimes seem to be almost keeping pace with the cheats, as far as we know. Anyway, it's improved. In 2010, CERA in particular and microdosing generally are the in-vogue cheating methods -- both subtle boosters aimed at long-term performance. If your big targets are the classics, why risk it all for these marginal, long-term gains that probably won't make a difference on the Muur? Why spend the money? Intuitively, to an admitted outsider, it doesn't make sense.
Of course, that could all change when gene therapy -- the PED of the future -- hits. Is gene therapy a Jetson's-like futuristic fantasy (think jetpacks and flying saucers), or sometime soon will I be able to chop off my legs and regrow them with Boonen-esque thighbones derived from DNA taken off his water bottle? I'm sure we'll find out eventually. For now, though, my optimism about the state of my favorite part of my favorite sport is slowly rising.