APOE-ε4 is the high risk variant of the APOE gene, the gene most associated with increased risk for late-onset Alzheimer's disease. Wikipedia shows that it is not a direct determinant of the disease - at least a third of patients with Alzheimer's disease are APOE-ε4 negative and some APOE-ε4 homozygotes never develop the disease. Yet those with APOE-ε4/APOE-ε4 have ~20x risk of developing Alzheimer's.
More information about APOE-ε4 is well explained at this blog post.
APOE-ε4 is notable as being the variation that James Watson requested not to learn when having his genome sequenced. User:Steven Pinker also requested that ApoE information be removed from his PGP10 data. In this way it has become a useful reference point when talking about genetic information that some people do not desire to learn. It is used as a reference point in the magnitude scale used within SNPedia.
It has been associated for over 20 years in a dose-dependent manner with increased total and LDL-cholesterol levels, and thus increased risk for heart disease and myocardial infarctions. [PMID 3698268]
[PMID 17192785] The researchers found that on testing DNA samples from 1,086 well-characterized Alzheimer's disease cases, a single SNP (rs4420638) lying 14 kb distal to the ApoE locus has a powerful association with late-onset AD (corrected p value was 5.3 x 10 e-34). No other SNP showed as robust an association. The authors estimated that people with two APOE-ε4 copies have a 25-fold increased risk for developing the disease compared to ApoE3/ApoE3 carriers. 
APOE-ε4 carriers may have their risk of developing Alzheimer's disease modified by SNPs elsewhere in their genomes. For example:
- rs2373115, a SNP in the GAB2 gene
- Inheritance of the rs1799724(T) allele appears to synergistically increase the risk of Alzheimer's in APOE-ε4 carriers and is associated with altered CSF Abeta42 levels [PMID 15895461]
- A haplotype of 3 SNPs in the POLD1 gene; the combined presence of this POLD1 I-G-T haplotype and the APOE-ε4 allele almost doubles the risk of AD (odds ratio: 10.09, CI: 3.88-26.25, =<0.0001) compared to APOE-ε4 carriers alone.[PMID 17498878]
- rs638405, a SNP in the BACE1 gene
The original patents covering the utility of APOE-ε4 genotyping to predict Alzheimer's disease have been (controversially) exclusively licensed by Duke University to Athena Diagnostics; these include patent nos. 5,508,167 (issued April 16, 1996, implying expiration April 16, 2013), 5,716,828 (issued Feb. 10, 1998), and 6,027,896 (issued Feb. 22, 2000).