Since the first spacewalks were performed, have there been any spacecraft that didn't allow for a spacewalk?
If you give "the first spacewalk" as your starting point, then we're looking at flights on or after March 18, 1965. As far as I can tell, the answer is "no", for reasonable values of "spacecraft" and "configured for a spacewalk".
Gemini, Apollo, and the Space Shuttle were all capable of performing EVA: they had systems for performing a controlled depressurization, a hatch that could be opened and closed in flight, and air reserves to repressurize. Any given mission might not have the ability to perform EVA (eg. because the crew aren't equipped with appropriate suits), but the spacecraft were capable of it.
SpaceShipOne and SpaceShipTwo are incapable of EVA, but since they are strictly suborbital, this lack of capability isn't very interesting.
On the Russian/Soviet side of things, all generations of the Soyuz and the related Chinese Shenzhou space capsules appear to be EVA-capable. Much like Gemini and Apollo, they depressurize the entire spacecraft for EVA.
Prior to your starting date, the Mercury spacecraft were fundamentally incapable of EVA: the hatch was bolted in place after the astronaut entered. The Soviet Vostok craft appear to have had the same restrictions. Voskhod 1 relied on air circulation to keep equipment cool; depressurizing it for EVA would have caused overheating. Other than that, every spacecraft that has carried humans into orbit has at least in theory been capable of performing a spacewalk.
Generally the question is, does the vehicle have an airlock.
The Space Shuttle was probably the only one that had a truly dedicated airlock.
Soyuz with two habitable modules, could depressurize the orbital module then open the outer hatch for space walks. Does that count as an airlock? Maybe, but a bit fuzzy. (The Chinese Shen Zou is very similar to the Soyuz).
Thus the question is, if there is no airlock, can you depressurize the vehicle so you can open the only hatch for an EVA. Or will that damage the vehicle? Are there sufficient air reserves to allow this?
Gemini just opened the hatch after depressurizing the vehicle. Voskhod had an inflatable airlock. (Vostok and Mercury did not do space walks I believe). (Hat top RussellB/Uwe!)
Since the question in the title is slightly different than the question in the body, it is perhaps worthwhile to look at the mission timelines:
"Since the Mercury program" then includes the flights of Vostok 5, Vostok 6 and Voskhod 1, none of which were configured for spacewalks.
One issue with the Apollo spacesuits was the visor assembly. The bubble helmets were always with the astronauts and their spacesuits. However, the visor assembly was a separate item that went over the helmet, with a gold mirror coating and various sunshields to protect from blindness and sunburn. A spacewalk without them would be theoretically possible, but dangerous.
Apollo 7 and 8 had no visor assemblies at all.
Apollo 9 and later launched with 2 visor assemblies, in the lunar module. Thus, a spacewalk was not safe until the CSM docked with the LM.
The two visor assemblies were taken down to the Moon, leaving the CM pilot without a visor during this time and making a spacewalk by the lone CM pilot unsafe.
Apollo 9 disposed of the visor assembles and PLSS's when the LM was discarded in Earth orbit. Apollo 10 discarded these items with the LM in lunar orbit. Apollo 13 discarded these items with the LM upon return to Earth. Apollo 11, 12, and 14 discarded the visor assemblies and PLSS's before taking off from the Moon. Spacewalks were no longer safe after these events.
Apollo 15 to 17 discarded the PLSS's before taking off from the Moon, but did carry the visor assemblies back to the CM, where they were used for the SM EVA. They were eventually brought back to Earth. Thus, a spacewalk would have been safe at any point after the first LM docking.