I recently started work on a program to write pinyin nicely to Chinese text. In order to test whether it corrected add tone marks to all possible pinyin, I worked through a table of pinyin and was surprised by some of the valid pinyin, which I've not come across before.
Pinyin ending in -en
Initials: d, t, n, l
There are many words ending in -en, but there are gaps in my table corresponding to ten and len. There was an entry for den, although there was no such word on MDBG. According to cojak.org, 扽 (to move, shake) can be pronounced dèn, but dùn is the normal reading. Similarly, 参 (to participate) can be pronounced dēn (also sān, shēn, cēn or sǎn), but is normally cān, which is how I learnt it. There was also an entry for nen, for which there is a single word on MDBG: 嫩 (nèn; tender or inexperienced).
Initials: z, c, s
Other than the very common word, 怎 (zěn; how), there is only one other zen word on MDBG: 谮 (zèn; to slander). As I mentioned above, 参 can be pronounced cēn according to cojak.org, but MBDG lists just three words: 岑 (cén; small hill), 涔 (cén; overflow, rainwater) and 嵾 (cēn; uneven). Finally, I had known one sen word: 森 (sēn; forest), and it seems there is only one other word: 椮 (sēn; lush growth).
Pinyin ending in -ei
There is a single character pronounced ei: 诶, which means "hey" and can have any tone. According to MDBG, the meaning are: ēi - to call someone; éi - to express surprise; ěi - to express disagreement; and èi - to express agreement. It is debatable to what extent these are really words.
Initials: g, k, h
When I was first learning Chinese, I noticed, that while 给 (gěi; to give) is very common, it is the only Chinese word pronounced gei. There is also only one word pronounced kei: 克 (kēi; to scold, beat; more commonly pronounced kè and meaning gram or to restrain). There are two words pronounced hei: 黑 (hēi; black) and 嘿 (hēi; hey), which I suspect is more modern.
Initials: zh, ch, sh
Like 给, both 这 (zheì or zhè; this, here) and 谁 (shéi; who) are very common words with unique pronunciations. There is no word pronounced chei.
Initials: z, c, s
There are no words pronounced cei or sei, but there is one pronounced zei: 贼 (zéi; thief, deceitful).
Initials: d, t, n, l
Again, like 给, 得 (děi; must, ought to), is common and unique. Like 这, 哪 (nǎ; which) has an alternative ei-pronunciation: něi. There are two other nei words, both quite common: 内 (nèi; inside) and 馁 (něi; hungry). There are many words pronounced lei but none pronounced tei.