Accent

Also known as: 口音 (kǒuyīn).

Even if a Chinese speaker is speaking standard Mandarin, certain pronunciation choices will result in some kind of accent.

Accent Features

Examples of accent features include:

presence or absence of er-hua
prominence of the final "-ng" consonant
word choice (e.g. 花菜 (huācài) vs. 菜花 (càihuā), 轻轨 (qingguǐ) vs. 捷运 (jiéyùn), etc.)
use of modal particles (啊 (a), 呗 (bei), 啦 (la), 哦 (o), etc.)

Having an accent does not necessarily mean a speaker's Mandarin is not "standard"; it means that the speaker's Mandarin has been influenced by the region where the speaker comes from (which is true of pretty much everyone's Mandarin).

Strong Accents

That said, there is such thing as a "strong accent" in Mandarin, which typically means "non-standard." Some features of strong accents include:

weird tones
sound substitutions (e.g. "-n" for "-ng," etc.)
difficult to understand word choice (because the speaker doesn't realize that a word or expression he is using is not widely understood outside of his region)
strange grammar

Certain accents have well-known features, and advanced learners of Mandarin Chinese can learn these features to improve communication with speakers of non-standard Mandarin.

Northern Mandarin

Extensive use of [er-hua]
Pronounced syllable-final "-ng"
Lack of social stigma (because Beijing is the cultural center of mainland China)

Dongbei Mandarin

Extensive use of [er-hua]
Pronounced syllable-final "-ng"
Non-standard tones

Shandong Mandarin

Non-standard tones

Southern Mandarin

Syllable-final "-ng" sounds often pronounced as "-n"
Initials zh-, ch-, sh- pronounced as z-, c-, s-
Relative lack of er-hua

Sichuan Mandarin

Initials zh-, ch-, sh- pronounced as z-, c-, s-
Relative lack of er-hua

Hunan Mandarin

Syllable-final "-ng" sounds often pronounced as "-n"
Initials zh-, ch-, sh- pronounced as z-, c-, s-

Fujian Mandarin

Syllable-final "-ng" sounds often pronounced as "-n"
Initials zh-, ch-, sh- pronounced as z-, c-, s-
Initial n- pronounced as l-
Relative lack of er-hua

Taiwanese Mandarin

Syllable-final "-ng" sounds often pronounced as "-n"
Initials zh-, ch-, sh- pronounced as z-, c-, s-
Relative lack of er-hua
Relative lack of neutral tone

Guangdong/Hong Kong Mandarin

Initials zh-, ch-, sh- pronounced as z-, c-, s-
Relative lack of er-hua