There are three types of IPv6 addresses:

Unicast - An IPv6 unicast address uniquely identifies an interface on an IPv6-enabled device.
Multicast - An IPv6 multicast address is used to send a single IPv6 packet to multiple destinations.
Anycast - An IPv6 anycast address is any IPv6 unicast address that can be assigned to multiple devices. A packet sent to an anycast address is routed to the nearest device having that address.

IPv6 does not have a broadcast address. However, there is an IPv6 all-nodes multicast address that essentially gives the same result.

Unicast IPv6 addresses

Global unicast - similar to a public IPv4 address. These are globally unique, Internet routable addresses. Global unicast addresses can be configured statically or assigned dynamically.
Link-local - Link-local addresses are used to communicate with other devices on the same local link. With IPv6, the term link refers to a subnet. Link-local addresses are confined to a single link. Their uniqueness must only be confirmed on that link because they are not routable beyond the link. In other words, routers will not forward packets with a link-local source or destination address.
Loopback - represented as ::1/128 or just ::1 in the compressed format
Unspecified address - ::/128 or just :: in the compressed format. It cannot be assigned to an interface and is only be used as a source address. It is used as a source address when the device does not yet have a permanent IPv6 address or when the source of the packet is irrelevant to the destination.
Unique local - some similarity to RFC 1918 private addresses for IPv4, Unique local addresses are used for local addressing within a site or between a limited number of sites. These addresses should not be routable in the global IPv6. Unique local addresses are in the range of FC00::/7 to FDFF::/7.
IPv4 embedded - used to help transition from IPv4 to IPv6

IPv6 network addresses