Cinnamontoast
Fais pas chier!
PMSL ^^ These people who won't link the relevant dog's health tests because they think we're nosy-hilarious! No way do the people charging silly money for silly crosses health test-that would eat into their profit! 
Most of the puppy farmers that were producing Puggles a few years ago seem to have moved on to "rare" coloured bulldogs and other crosses. Some still do the cross and have flash websites with outright untruths to fool the gullible puppy buyer.
Amazing how these sites rarely show adult puggles?
A google image search soon shows why.
There are a lot of pug crosses in rescues.
Don't know a huge amount about these type of dogs, but having googled images of the adults, some where rather nice looking.
Genuinely interested in why they are not a good thing
Getting up at 5 am and you didn't read the whole thread, C! Beagles=hunters. Pugs=brachycephalic (flat faced) Pugs often have breathing issues so to mix the two is not a good idea, won't improve the breed etc because you may end up with a brachycephalic dog who wants to go off and hunt and suffers because it can't get enough oxygen.
It's also rare (although not unheard of) for those who breed 'designer' dogs with daft names to carry out proper health testing (the appropriate breed tests as recommended by the KC) because it equals less money for the breeder.
Charging silly money is unjustified but typical for 'designer' breeds, mainly because they have stupid names. Back in the day, these pups would be free to good homes as an 'oops' litter.
This is from Wikipedia, which as we know in AAD is not necessarily the best sourcebut it does mention potential health issues:
Puggles are not necessarily healthier than their parent breeds.[7] Both Beagles and Pugs can suffer from cherry eye and epilepsy. Puggles can also inherit hip dysplasia from one or both of their parents. Some Puggles can suffer from food and environmental allergies. If the allergies are serious enough, a special diet or steroid shots may be needed.
Puggles who have longer snouts like the Beagle parent are at a reduced risk of respiratory problems. However, Puggles can suffer from the respiratory ailments commonly found in Pugs (a breed known for being brachycephallic), which can be problematic. One common, nonthreatening respiratory ailment that Puggles sometimes suffer from is reverse sneezing (also called backwards sneezing or inspirational paroxysmal respiration).
This gives a decent account of the Cesky terrier start up - http://www.cesky-terrier-club.co.uk/html/history.html and you will find similar for the Eurasier.
The difference between this & the fad breeding is the aim & purpose of the new type and that the early generations are all kept and assessed and bred on if they have desirable traits or are discarded from the breeding pool. They are not called anything but crosses for quite a few generations & no money was made.
This gives a decent account of the Cesky terrier start up - http://www.cesky-terrier-club.co.uk/html/history.html and you will find similar for the Eurasier.
The difference between this & the fad breeding is the aim & purpose of the new type and that the early generations are all kept and assessed and bred on if they have desirable traits or are discarded from the breeding pool. They are not called anything but crosses for quite a few generations & no money was made.
So the biggest issue then is not that people are crossing breeds per se but that they are making money from it?