Though jeans and sneakers are quite common in IT offices, more traditional clothing (like business attire, smart casual or business casual) is sometimes required. While it is not that difficult to find a suit that fits those codes, it is much more difficult to choose shoes which fit the clothing and someone’s style.
The following list is by far not exhaustive and may contains misinformation. Use at your own risk :) .
The probably most formal shoe is the Oxford, a model with a closed lacing.
The Monk is a moderately formal shoe. Instead of laces, it provides a buckle. Bob Getty provides some pictures of a polished cordovan monk.
The Derby is a model whith an open lacing. The back quarters of the shoe are laid on the front vamp. The shoelace eyelet tabs are part of those.
The Derby is quite versatile and may be used with business suits as well as with jeans.
Though it mainly is a shoe for men, it sometimes is offered to women also.
The Blücher (or Blucher) is a model whith an open lacing like the Derby. Unlike the Derby it consists of a one-cut vamp, while the shoelace eyelet tabs are applied to it. The typical derby bow is missing:
The terms Blücher and Derby are often used synonymously, despite those differences.
The Norwegian, which seems to be more common in germany and france than in great britain, is a model whith an open lacing and the shoelace eyelet tabs being part of the back quarters, similar to the Derby. A typical characteristic is the vertical weld at the shoe’s tip and the additional vamp above the toes.
The shown variants are not formal shoes and thus worn during spare times (or maybe during Casual Fridays). The french, more formal variant (no figure available) with less explicit welds may be more acceptable.
Instead of a leather sole, there are also rubber sole variants for outdoor use.
Chelsea boots provide an elastic siding and are used by both women and men.
Both penny and tassel loafers are shoes mainly worn during times of leisure.
Brogue shoes are known in a couple of variants, e.g. halfbrogues, fullbrogues and longwings. A brogue may nowadays be a traditional shoe (like oxford, derby, or monkstrap) “that includes or evokes the multi-piece construction and perforated, serrated edges characteristic of brogues”. The figure shows a traditional fullbrogue Oxford in oxblood.
The german wikipedia article states that a halfbrogue may be acceptable for business wear, while the fullbrogue is not.
Traditional shoes mainly consist of leather, even the insole and the midsole. The outsole usually consists of leather as well, sometimes including some brass nails to increase the abrasion resistance. Some variants use rubber as the material of the outsole.
Business shoes tend to be of black color. A couple of proverbs (»no brown in town«, »no brown after six«) express this habit. Nevertheless brown (e.g. italian) shoes sometimes are combined with black, grey, or even navy colored suits. The following figure shows the black norwegian model depicted above in brown color.
A couple of base shoe models exist. Some of them are more acceptable for business dress codes than others.
Many shoes on the market do not follow those plein types, but are derived from those. Finally, it is a matter of an individual’s taste which shoes to use.
 The german wikipedia articles about the Derby, the Blücher, and the Norwegian provide more details than the english pages.