There's no "Best" B/W film as different B/W films have very different characteristics in terms of image structure (granularity, tonality etc). Couple this with the myarid ways you can process a roll of B/W film by choosing different developers, dilutions, processing times and temperatures to create even more combinations of texture, acccutence and so on. Then add the variables you can change at the enlarger, eg: paper type, dodging, burning, preflashing and a host of processing methods and the whole question you ask becomes very blurred indeed.
There are a few emulsions however that are in a class of their own, these are:
Kodak Tech Pan:
The sharpest most grainless film available to the general market (there are sharper films in B/W but they are specialist film and VERY hard for consumers to come by). It's a pig to develop in Kodak Chemistry, however using Rodinol makes matters a lot easier. Near Grainless 20x30" prints can be made. Exposure and development is highly critical and I won't recommend this film to a novice.
Agfa APX-25
Landscape and portrait film, Slow at 25 ISO and one of the slowest films ever produced (6 ISO Kodak plates were the slowest). Superb when printed on high quality papers. Reasonably easy to develop and exposure tolerance was pretty good.
Sadly Agfa dropped this film in 2001 much to the disgust of many B/W photographers.
Ilford Pan F Plus
The only emulsion that seriously rivals Kodak Tech Pan for granularity and sharpness. When used properly and processed carefully this film is capable of awsome performance. It's slow, 50 ISO and has the most wonderful tonality when used for portraits and architectural/landscape work. Highight and shadow detail are stunning. Pan F is excelelnt for wildlife and panning race cars (motorsports).
Ilford Delta 100
Not a film for the novice. Delta Professional is highly exposure critical with a very low exposure latitude so exposures must be bang on the money or the film will punish the photographer by giving horrible results. When processed correctly this film is near grainless, contrasty and has a slight luminescense to it that the kodak T-max lacks. It's highlight and shadow detail capablities are supers.
Ilford Delta 400 Professional
A superb portrait emulsion. Crisp and damn near grainless. Outperforms T-Max 400 in all respects.
ID-11 developer at 1:3 at 20C gives wonderful results.
Ilford Delta 3200 (rated at 3200 ISO).
This film when exposed properly and processed with care simply blows people's minds. It can give stunning results for a fast film, but don't make any mistakes as it's a very unforgiving film. One mistake and the results are tennis ball grain and awful prints. When used properly you get really low almost grainless 4x6" prints and 8x10s with less grain than Tri-X at 400 ISO.
Kodak Tri-X
A venerable film that's been in production for 48 years. Golfball sized grain and high contrast levels make this film the film of choice when trying to duplicate the look and feel of 60s Fashion and Photojouralism shots. The grain is LARGE but unlike more modern emulsions it's not a visually horrific granularity. Easy to work with, easy to develop and is great for High Key lighting.
Ilford HP5 Plus.
Great film for the novice in the 400 ISO speed class. As Sriram puts reviews it well no more comments are needed from me about it.
Agfa APX-100
Great stuff for studio work when Delta 100 isn't available. A bit less sharp and has it's own unique tonality that is excellent with light skins. Good exposure latitude.
C41 Chromogenic emulsions:
Kodak TC400N - Very popular 400 ISO film. Gives good results and is nearly grainless due to using dye instead of silver halides. I find it needs 1/2 to 3/4 of a stop additional exposure.
Ilford XP/2 Super.
XP2 was the original Chromogenic film released nearly 20 years ago and it's replacement is wonderful. I prefer it to the Kodak offering but from what I've been told it's hard to come by in Singapore.
In general I avoid chromogenic emulsions and stick to traditional B/W emulsions unless a client needs the film processed very quickly. Chromogenic films when printed on colour paper at labs that don't have a 'channel' set up for B/W chromogenic films give wierd colour shifts that are unpredictable to say the least.