For fusion bombs (i.e., hydrogen bombs) as opposed to fission bombs (atomic bombs, Hiroshima-type) there is likely no theoretical upper limit, apart from gravitational collapse of the material into a black hole. As long as one can provide enough fuel (namely, hydrogen), it will explode. A fusion explosion is in fact a similar mechanism to that of a Supernova type Ia, which occurs when a white dwarf has accreted enough material to explode. Such a white dwarf can be larger than our sun - the theoretical limit is about 1.4 times the mass of our sun, as above this it will collapse by its self-gravity. There is no way anyone could collect as much as the solar mass of hydrogen and put it into one bomb...
So the question is really technical in nature. Fission bombs are typically not very large (relative...), due to the need to ensure sub-critical mass before the actual explosion. However, this limit does not exist in fusion bombs, as there is no critical mass there - you can put in as much hydrogen as you want, and once it ignites it will explode.
The most powerful man-made bomb that was exploded is known as the "Tsar bomb", a hydrogen bomb that was detonated by the Soviet Union on Oct. 30th, 1961. This bomb had a yield of 50 mega-ton TNT. This is about 10 times the combined energy of all conventional explosives used during world war II, or about 1570 times the combined energy of the bombs that destroyed Hiroshima and Nagasaki.
As an outcome of this detonation, all buildings in the village of Severny (both wooden and brick), located 55 kilometres from ground zero within the Sukhoy Nos test range, were destroyed. In districts hundreds of kilometers from ground zero wooden houses were destroyed, stone ones lost their roofs, windows and doors; and radio communications were interrupted for almost one hour. One participant in the test saw a bright flash through dark goggles and felt the effects of a thermal pulse even at a distance of 270 kilometres. The heat from the explosion could have caused third-degree burns 100 km away from ground zero. A shock wave was observed in the air at Dikson settlement 700 kilometres away; windowpanes were partially broken to distances of 900 kilometres. Atmospheric focusing caused blast damage at even greater distances, breaking windows in Norway and Finland. Despite being detonated 4.2 km above ground, its seismic body wave magnitude was estimated at 5-5.25. Sensors continued to identify the shockwaves after they had circled the earth twice.
The largest US nuclear test was "Castle Bravo", which was detonated on March 1st, 1954 in the Bikini atoll. It was "only" 15 Megaton, about 1/3 of the Soviet's largest explosion.
So, technically, it is certainly possible to build bombs as strong as one wants; but why spend the money on doing that, if one can already destroy the entire human race with existing nuclear weapons?