You have options. Numerous crimes merited the death penalty, from murder and treason(which could be something as simple as denying Elizabeth as head of the Anglican Church), to buggery and hawk theft. You would most likely be hanged, but if you wanted to get a notable death you could commit treason, and be drawn and quartered. Or you could poison somebody, or commit heresy, which made you liable to be burned alive.
Contrary to our expectation of society progressing constantly, by Victorian England, there were 222 crimes that could get a man hanged, known as the "bloody code".
Crimes that warranted capital punishment ranged from what you would expect, like murder, to stealing from a rabbit warren.
The expansion of capital offenses, from 50 in 1688 to over 200 in 1820, was largely due to an increase in property crimes punishable by death. This is largely regarded as an effort by landowning classes to protect their status, and the name "bloody code" was coined by reformers who saw the addition of seemingly minor crimes as unfairly cruel.
However, it must be noted that most people condemned to death were not executed. For instance, between 1770-1830, over 35,000 people were condemned to death in England and Wales, yet only 7,000 were actually executed. This was due to the power of judges or jurors to lessen or commute the sentence of the defendant.
So, in short, if you really wanted to die, you had options, and more were coming.