Transmission of the bacterium that causes Lyme disease is well understood to require a substantial feeding period. In general, soft ticks (Argasidae) transmit pathogens within minutes of attachment because they feed more frequently, whereas hard ticks (Ixodidae) take hours or days, but the latter are more common and harder to remove.For an individual to acquire infection, the feeding tick must also be infected. Not all ticks are infected. In most places in the US, 30-50% of deer ticks will be infected with Borrelia burgdorferi (the agent of Lyme disease). Other pathogens are much more rare. Ticks can be tested for infection using a highly specific and sensitive qPCR procedure. Several commercial labs provide this service to individuals for a fee. The Laboratory of Medical Zoology (LMZ), a nonprofit lab at the University of Massachusetts, provides a comprehensive TickReport  for a variety of human pathogens and makes the data available to the public. Those wishing to know the incidence of tick-borne diseases in their town or state can search the LMZ surveillance database. Examples
Major tick-borne diseases include:

Bacterial
Lyme disease or borreliosis
Organism: Borrelia burgdorferi sensu lato (bacterium)
Vector: at least 15 species of ticks in the genus Ixodes, including deer tick (Ixodes scapularis (=I.
spinipalpusm, Dermacentor andersoni, and D. variabilis
Endemic to: North America and eastern Russia
Colorado tick fever
Organism: Colorado tick fever virus (CTF), a coltivirus from the Reoviridae
Vector: Dermacentor andersoni
Region: US (West)
Crimean-Congo hemorrhagic fever
Organism: CCHF virus, a nairovirus, from the Bunyaviridae
Vector: Hyalomma marginatum, Rhipicephalus bursa
Region: Southern part of Asia, Northern Africa, Southern Europe
Severe febrile illnessOrganism: Heartland virus, a phlebovirus, from the Bunyaviridae
Vector: Lone star tick (Amblyomma americanum)
Region: Missouri and Tennessee, United States
Severe febrile illness, headaches, coma in 1/3 patientsOrganism: tentatively Alongshan virus, jingmenvirus group in the flavivirus family
Vector: tick (likely Ixodes persulcatus, Ixodes ricinus), mosquitoes
Region: Inner Mongolia but potentially more widespread

Protozoan
Babesiosis
Organism: Babesia microti, Theileria equi
Vector: Ixodes scapularis (deer tick), I. pacificus (western black-legged tick)
Region (US): Northeast, West Coast
Cytauxzoonosis
Organism: Cytauxzoon felis
Vector: Amblyomma americanum (Lone star tick)
Region (US): South, Southeast

Toxin
Tick paralysis
Cause: Toxin
Vector (US): Dermacentor andersoni (Rocky Mountain wood tick), D. variabilis (American dog tick or wood tick)
Region (US): D. andersoni: East, D. variabilis: East, West coast
Vector (Australia): Ixodes holocyclus (Australian paralysis tick)
Region (Australia): East

Allergies
Alpha-gal allergy - Alpha-gal syndrome is likely caused by a hypersensitivity reaction to the Alpha-gal (Galactose-alpha-1,3-galactose) sugar molecule introduced by ticks while feeding on a human host. The immune reaction can leave people with an allergy to red meat and other mammalian derived products.