Most modern PVA's/yellow glues etc. are completely capable of handling most woodworking tasks. Specific projects may require specific adhesives and are thereby limited in scope due to the nature of the task at hand or the demands placed upon the adhesive itself. Waterproof vs. water resistant, flexible vs. rigid etc. etc. etc.. The issue of glue lines can be as much a matter of the materials being used as it is the glue and its application. When the brand of glue and to a certain extent the type of glue are not a real issue its a good idea to have a test board around with dried samples. A couple years back I posted a test board with I think it was 10 or so different common glues. Most of which came out of the big box stores and the remainder were PVA's used for inlay work. The variation in color once dried was rather surprising to say the least.
Addressing Bob's original question, speaking for myself I have come to expect a certain amount of "squeeze out". A very limited, very small amount of squeeze out! This lets me know I've used enough glue to have at least mated the two surfaces being glued together. Too much glue and you just end up with a mess and the very likely hood of the pieces slipping or sliding over one another during clamping. A minimal amount of glue also gives the advantage of friction fitting the two pieces together. Too much glue and you'll be rubbing em together forever.
I address the squeeze out clean up by using more often than not a small card scrapper to collect the most of it, then I take a 'damp' and I do mean just 'damp' rag and wipe off the remaining glue THOROUGHLY. I personally have had great success doing it this way and I've never have had a glue failure. The card scraper works well on inside corners as well.
Glue lines on dark woods and contrasting woods are relatively easy to hide by their nature alone. LIghter woods present a problem alot of times, especially with dark drying adhesives. Maples, populars, ash etc. can usually require extra efforts. First things first, you have got to have crisp clean cuts to start with. The glue surfaces have to be parallel to one another. I've played around with mating a 90* face to an 88* face with the bevel facing out and have had pretty good luck, Clamping will usallly compress the two together well enough that the glue bond more than sufficed especially on soft woods like popular. BuT, that was/is an awful lot of farting around, more than I'd wanted to get in the habit of doing. Focus on just good clean cuts. Chip out is another reason glue lines can be pronounced, miters that are just a couple of 10ths of a degree off will give you lines.
When I do have a problem with glue lines I've played around and have found that by wiping down the faces of the glued pieces with again just a "damp" rag, waiting a few seconds and then using 320 sand paper to sand the entire area creating a slurry that the fine sawdust will work its way into the glue and create an almost invisible fix. If need be, a dab of glue is applied and the process goes forward. Sanding until all of the additional glue has been absorbed by the slurry. I don't seem to have as good of luck with 220 or 180 grits..but that may just be me. I've also used a slurry made up and then applied to the surface. A dab of glue, a couple drops of water mixed and applied. I've had so/so luck with that process. I think its more a matter of the mix ratio than anything else I need to work on and the fineness of the sawdust. In cases where the glue line was jussssssssssssssssst barely visible I've had good luck with taking artists pencils and drawing in grain lines or continuing them on etc., Slivers of like wood wood great on box joints and dovetailed joinery gaps. Cut or sanded wedges have a small amount of glue applied and then tapped into position. If after that, I still have a line, then its off to play B..or C..*L*
If you have the ability to expand/magnify the attached pitchers look for the "patches". The nite stand, while simple in design was an exercise in getting it right, tight joints, exact dimensions etc...In the end I fell short in only a couple of spots where the joints were not perfectly seemless..
"..... limited only by imagination"
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Skipper the Penguin