Do people wake up faster with inconsistent alarm sounds? Many people have one alarm clock sound that wakes them up every morning. 


Is having this consistent sound the optimal way to wake someone up? 
Or can you startle someone faster by changing to a different sound clip every day? 


Assume the alarm clock is going off at the same time every morning.
A general model of processing stimuli suggests that when information does not provide informational value, then we gradually begin to ignore it. Such a model is consistent with the experience of many people in relation to background traffic noise when moving from a quiet to a noisy neighbourhood. I.e.,  the frequency with which external traffic noise enters into personal awareness gradually decreases over time.

Habituation to traffic noise while sleeping

It seems that there is quite a lot of research on the effect of traffic noise on quality of sleep and the role of habituation (see this google scholar search on "habituation to noise sleep").

Kawada (1995) provides a review of the effect of traffic noise on sleep. Specifically in relation to habituation the author wrote:


  Habituation to noise:  Views and opinions on this parameter differ. Thiessen et al. reported habituation to intermittent
  wakefulness10～12. In their study, subjects were exposed to passing
  truck noise less than 20  times a night with a peak level of 65 dBA.
  The  probability of a shift to shallower sleep and the  amount of deep
  sleep demonstrated failure of adaptation over 24 successive nights.
  The probability of awakening decreased by almost one  half in two
  weeks. Griefahn also studied  habituation of 36 students to 
  high-density road  traffic noise and detected an all-night effect of 
  noise on sleep for 12 consecutive nights13. Deep  sleep was prolonged
  and shallow sleep including  intermittent wakefulness became
  progressively  shorter at 37 to 63.5 dBA. Vallet at al. indicate  that
  there is no habituation to noise14. According to experiments on
  subjects living in a noisy  environment for more than four years,
  young  subjects showed less deep sleep and older subjects, less REM
  sleep under conditions of silence.  Both Di Nisi et al. and Ohrstrom
  reported that  there seems to be no habituation to noise 
  exposure15,16. They exposed subjects to randomly distributed noise
  and it was impossible to  predict either the time of exposure or the
  type of  noise presented. Kawada and Suzuki could find  no definite
  habituation to a noisy environment17.  Their interval of noise
  exposure was 15 minutes  and there was only one pattern of passing
  truck  noise. Essentially the same noise characteristics  are reported
  by Thiessen, but the findings differed from each other. Based on
  inter-individual  variation in sensitivity to noise, habituation 
  should differ according to the person.


I find this summary a little confusing. The between subject studies are not especially relevant in that habituation should presumably reduce the disruption caused by noise, but not necessarily remove the effect. Thus, it seems like longitudinal evidence would be the most relevant.

General review of noise on sleep

Muzet (2007) provides a relatively recent review of research on the effects of environmental noise on sleep.
With regards to habituation the author wrote:


  [Autonomic responses, such as heart rate changes and vasoconstrictions
  in response to noise while sleeping] have bee found not to habituate
  over long exposure times compared with clear subjective habituation
  over successive noise-exposed nights.


Research on alarm clocks

I found an article by Moorcroft et al (1997) that discussed the role of alarm clocks in peoples awakening process


  The ability to awaken oneself from sleep at a preselected time without
  external means (such as alarm clocks) was studied using, first,
  subjective and, second, objective methods. First, in a telephone
  survey of 269 unselected adults, over one-half said that they never
  use an alarm clock (or other external means) or always awaken before
  it. Another 24% said that they sometimes awaken before the alarm.
  Furthermore, this ability positively correlated with age and was
  related to consistency in the amount of nightly sleep but not
  consistency in wake-up time. Second, 15 people who said they regularly
  self-awaken were objectively tested for this ability in their own beds
  using actigraphy for three consecutive nights while choosing their own
  wake-up times. Five awoke within 10 minutes of their target time
  (mostly before) on each night, five did so on two of the three nights,
  and of the remaining five, four did so on one night. Choice of target
  times varied considerably within subjects but more so for those who
  were more successful. Taken together these results show that many
  people have the ability to regularly awaken themselves from sleep at a
  desired time and that such an ability is of practicable utility.


Does having a consistent alarm clock decrease ability to wake up

I haven't found any specific empirical data on your question.

Habituation processes would suggest that a consistent noise that is deemed to carry a lack of informational content will gradually be more frequently ignored, and thus an inconsistent noise may be more effective in generating attention and perhaps wakefulness. That said, alarm clocks do carry informational content, and people could potentially tune themselves to that noise as the important noise to indicate the time to wake up.

References


[10] Thiessen, G.J.: Disturbance of sleep by noise, 
J. Acoust. Soc. Am., 64, 216-222 (1978).    
[11] Thiessen, G.J. and Lapointe, A.C.: Effect of 
intermittent truck noise on percentage of
deep sleep, J. Acoust. Soc. Am., 64, 1078-1080 
(1978).   
[12 Thiessen, G.J. and Lapointe, A.C.: Effect of 
continuous traffic noise on percentage of
deep sleep, waking and sleep latency, J. 
Acoust. Soc. Am., 73, 225-229 (1983).    
[13] Griefahn, B.: A critical load for nocturnal 
high-density road traffic noise, Am. J. Ind.
Med., 9, 261-269 (1986).    
[14] Vallet, M., Gagneux, J.M., Blanchet, V., 
Favre, B. and Labiale, G.: Long term sleep
disturbance due to traffic noise, J. Sound
Vib., 90, 173-191 (1983).    
[15] Di Nisi, J., Muzet, A., Ehrhart, J. and Libert, 
J.P.: Comparison of cardiovascular responses 
to noise during waking and sleeping in
humans, Sleep, 13, 108-120 (1990).    
[16] Ohrstrom, E. and Bjorkman, M.: Effects of 
noise-disturbed sleep: A laboratory study on
habituation and subjective noise sensitivity,
J. Sound Vib., 122, 277-290 (1988).  
[17] Kawada, T. and Suzuki, S.: Instantaneous 
change in sleep stage with noise of a passing
truck, Percept. Motor Skills, 80, 1031-1040
(1995). 
Muzet, A. (2007). Environmental noise, sleep and health. Sleep medicine reviews, 11, 135-142.
Moorcroft, W.H., Kayser, K.H. &amp; Griggs, A.J. (1997). Subjective and objective confirmation of the ability to self-awaken at a self-predetermined time without using external means. Sleep, 20, 40-45.