What sort of relationship do the worshippers have to the Vedic deities such as Indra, Agni and Varna? Looking ahead: Do you think it is similar to or different from the relationships to later deities (Shiva, Vishnu, Krishna)?
Well, the relationship between the Vedic Gods like Agni, Indra and the human beings is not that of a king and his subjects. The seekers or worshippers regard God Indra as their friend, father or son. This is an important aspect of the Vedas which needs to be stressed.
Following are few Veda mantras in support of my claim:
Indra is the friend who gives joy (mandayat sakham) -RV 1.4.7
Indra , we are seeking your friendship, we desire you alone- RV 10.133.6
O Indra develop in us the will power just as a father trains his son- RV 7.32.26
O Indra, coming together let us converse- RV 1.30.6
O Indra, you are superior to father or brother. You are same as my mother- RV 8.16
Similarly, there are many mantras which treat Agni as a dear friend and father. All 14 mantras of Sukta RV 1.94, for example, stress Agni's friendship. All these mantras end with the following prayer:
Samsad agne sakhye mA rishAma vayam tava |
O Agni, may we not suffer separation in our friendship.
So, apparently, Vedas are completely devoid of Bhakti (devotion) which is overwhelmingly present in the later day texts such as the PuranAs etc. But, on seeing closely we can still find traces of Bhakti in them too.
Another mantra worth noting here is the following which reiterates the relation that we share with the Vedic Deities:
Yuvoh hi nah saravyA pitrAni (1), samAno vandhuh (2), uta tasya vittam (3).
Between you (Gods) and us (1), there is ancestral friendship and we are equal as relatives (2); remember and give it regard.
In this answer RV denotes Rig Veda.
The relationship of Vedic deities and humans is reciprocal and complex. For example, a worshiper would sing songs praising the deity and offer grains, animal and the deity in turn return the favor with riches of the cattle, wealth and sons1
tám u stuṣa índaraṃ yó vídāno gírvāhasaṃ gīrbhír yajñávr̥ddham yásya dívam áti mahnā́ pr̥thivyā́ḥ purumāyásya riricé mahitvám
Him now I praise, Indra, who is wise, Brought by song, by means of songs, strengthened by worship; Of whom -- beyond heaven in greatness, wonderful -- The majesty exceeds the earth.
This relationship stems from the following verse from book X of Rigveda where God Indra says to poet that:
aháṃ dāṃ gr̥ṇaté pū́rvyaṃ vásu, ahám bráhma kr̥ṇavam máhyaṃ várdhanam (X, 49, 1) 'I shall give to the singer the ancient boon, I shall make prayer the means of growth for me'
I do not know what was the relationship with later deities